1 auxiliary appendix: instructions and items a

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AUXILIARY APPENDIX: INSTRUCTIONS AND ITEMS

A. Instructions provided to participants:

First instruction screen:

Welcome to the experiment! Your job is to judge the similarity of physics problems. You will be

shown a pair of physics problems and asked whether you think they would be solved similarly.

To respond, click the mouse on the white box for “Yes” or “No”. After you make your response,

you will be presented with feedback about the correctness of your choice. Sometimes you will be

asked to explain your choice by using the keyboard to type into a text field on the screen. Press

the spacebar to begin the experiment.

Second instruction screen (displayed after the completion of all items):

You are almost finished! This is the last portion of the experiment. On the next slides, you will

be presented with the names of 8 physics concepts or principles. Please rate on a scale of 1-5

how much you know or remember from class about each concept. A 1 means you know nothing

about that concept and a 5 means that you know a lot about that concept. A response in between

means that you know something about that concept. To respond, press the number on the

keyboard that corresponds with the rating. Press the spacebar to continue.

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B. Items used in the study

TABLE I. Distribution of problem pair types and topics for items #1-32. Each problem in a pair is designated by the letter a (Problem 1) or the letter b (Problem 2)a. Topic Surface Principles Both Neither Newton’s 2nd Law 1a, 2a 10b 17a, 17b,

18a 25a, 30b

Newton’s 2nd Law + centripetal acc.

4b, 5b 9a, 9b, 10a 18b 29b, 31b

Cons. of Energy 1b, 3a, 4a 11a, 11b 19a, 19b 26a

Work-Energy Thm 6a, 7b 12a, 12b 20a, 20b 25b, 27b

Cons. Of Momentum 2b, 3b 13a, 13b 21a, 21b 28a, 30a

Impulse-Momentum Thm

6b, 8b 14a, 14b 22a, 22b 26b, 32b

Cons. Of Angular Momentum

7a, 8a 15a, 15b 23a, 23b 29a, 32a

Angular Impulse-Angular Momentum Thm

5a 16a, 16b 24a, 24b 27a, 31a, 28b

aQuestions 20b and 25b could also be solved using Newton’s second law and the definition of work, but were still classified as work-energy theorem. Question 17b could be solved using the work-energy theorem, and question 14a could be solved with Newton’s second law.

TABLE II. Sparse feedback condition (N=13), average scores on each problem pair match type for the middle 32 items. Surface Match Yes No

Prin

cipl

e M

atch

Yes 0.77±0.04 0.55±0.05

No 0.59±0.05 0.79±0.04

TABLE III. Elaborate Feedback condition (N=13), average scores on each problem pair match type for the middle 32 items. Surface Match Yes No

Prin

cipl

e M

atch

Yes 0.81±0.04 0.53±0.05

No 0.47±0.05 0.73±0.04

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SURFACE ONLY MATCH 01) Problem 1 (Newton’s Second Law) Bungee 01

A 75-kg bungee jumper steps off of a 30-meter high bridge with a 13-meter long bungee cord tied to his ankles. The cord has a spring constant of 100 N/m. Calculate the acceleration experienced by the jumper when he is 9 meters above the water’s surface.

Problem 2 (Conservation of Energy w/springs) Bungee02 A 60-kg bungee jumper jumps from a bridge 31 meters above the water. She is tied to a 12-m bungee cord that has a spring constant of 50 N/m. Calculate the speed of the jumper when she is 5 meters above the water’s surface. Feedback: (Correct/Incorrect). These problems would NOT be solved similarly. Problem 1 includes acceleration so it would be solved using Newton’s Second Law. Problem 2 includes changes in height, spring stretch, and changes in speed, so it would be solved using Conservation of Energy.

02) Problem 1 (Newton’s Second Law) ShoppingCart01

While shopping you add a bag of dog food to your empty, stationary 14.5-kg cart. Then with a force of 12.0 N, you accelerate the cart at 0.6 m/s2. What is the mass of the dog food?

Problem 2 (Conservation of Momentum) ShoppingCart02 A shopping cart of mass 30 kg is rolling along a level surface at a speed 0.5 m/s. A 2-kg carton of milk is dropped from rest and lands on the cart. What is the final speed of the cart and the milk?

Feedback: (Correct / Incorrect) These problems would NOT be solved similarly. Problem 1 includes force and acceleration, so it would be solved using Newton’s Second Law. Problem 2 includes mass and change in speed with no external forces on the system, so it would be solved using Conservation of Momentum.

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03) Problem 1 (Conservation of Energy) Hawk01 A 1.5-kg hawk carrying a 0.5-kg fish in its talons flies over a lake at some angle with a speed of 2 m/s and a height of 6.0 meters. Suddenly, the fish slips out of the bird’s grasp and drops toward the water. What is the speed of the fish after it has fallen 3.0 meters?

Problem 2 (Conservation of Momentum) Hawk02 A 1.5-kg hawk searching for food sees a 0.1-kg mouse running on the ground below at 2.0 m/s. The hawk swoops down to follow behind the mouse at a speed of 4.0 m/s and grabs the mouse with its talons. What is the speed of the hawk with the mouse in its talons just after the capture?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes changes in speed and height, so it would be solved using Conservation of Energy. Problem 2 includes mass and change in speed with no external forces on the system, so it would be solved using Conservation of Momentum.

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04) Problem 1 (Conservation of Energy) Pendulum01

A 2.0-kg ball is tied on the end of a 0.5-m long string to make a pendulum. The pendulum is given a large shove and it swings in a complete vertical circle. If the mass has a speed 1.5 m/s at the top of its swing, how fast will it be going at the bottom of its swing?

Problem 2 (Newton’s 2nd Law with centripetal acceleration) Pendulum02 A 0.15-kg ball is tied on the end of a 1.10-m long string to make a pendulum. The pendulum is swung in a vertical circle. What is the minimum speed the ball must have at the top of its arc so that it continues moving in a circle without the string collapsing?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes changes in height and speed, so it would be solved using Conservation of Energy. Problem 2 includes force, speed, and circular path radius so it would be solved using Newton’s Second Law with centripetal acceleration.

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05) Problem 1 (Angular Impulse-Angular Momentum Theorem) An airplane propeller can be considered a long thin rod. If each of the two blades is 3.75 m long and has a mass of 160 kg, what angular impulse must the motor apply to bring the blades up to an angular speed of 30 rad/s?

Problem 2 (Newton’s 2nd Law with centripetal acceleration) An airplane is flying in a horizontal circle at speed 133 m/s with its wings tilted 40 degrees to the horizontal. Assume that the required force is provided entirely by an aerodynamic lift perpendicular to the wing surface. What is the radius of the circle in which the plane is flying?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes angular impulse and change in angular speed so it would be solved using the Angular Impulse-Angular Momentum theorem. Problem 2 includes force, speed, and circular path radius, so it would be solved using Newton’s Second Law with centripetal acceleration.

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06) Problem 1 (Work-Energy Theorem) Rifle01

The compressed air in an air-gun pushes a 0.15-kg plastic projectile a distance of 0.3 m with an average force of 44.5 N, giving it a velocity of 13.3m/s. How much work was done by the air-gun?

Problem 2 (Conservation of Momentum) Rifle02 A rifle has a mass of 4.5 kg and it fires a bullet of mass 10.0 g at a muzzle speed of 820 m/s. What impulse was delivered to the bullet by the gun?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes work and change in speed so it would be solved using the Work-Energy theorem. Problem 2 includes impulse, mass, and change in speed so it would be solved using the Impulse-Momentum theorem.

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07) Problem 1 (Conservation of Angular Momentum) RollingBall01 A bowling ball of mass 7 kg is thrown down the lane in such a way that it initially slides without rolling at 2 m/s. Some time later the ball rolls without slipping. What is the final speed of the bowling ball?

Problem 2 (Work-Energy Theorem) RollingBall02 A uniform ball of radius 15 cm and mass 6 kg is initially sliding at 3 m/s on a rough surface without rolling. Some time later, the ball rolls without slipping at speed 2 m/s. How much work was done on the ball by the rough surface?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes change in angular speed with no torque exerted by the floor on the ball at the contact point so it would be solved using Conservation of Angular Momentum. Problem 2 includes work and change in speed so it would be solved using the Work-Energy theorem.

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08) Problem 1 (Conservation of Angular Momentum) BulletBlock01 A 0.01-kg bullet of traveling with a speed 100 m/s is shot into the rim of a vertically mounted cylinder of mass 4.0 kg and radius 0.5 m. The cylinder is free to rotate about an axle through its center. The bullet enters the cylinder at an angle of 60o relative to the radius and comes to rest instantly. What is the final angular speed of the system?

Problem 2 (Impulse-Momentum Theorem) A bullet of mass 10 g is fired at 250 m/s into a solid block of mass 10 kg. The bullet takes 1 millisecond to come to a stop inside the block, which remains stationary. What was the impulse delivered by the block to the bullet?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes change in angular speed with no external torque on the bullet-cylinder system so it would be solved using Conservation of Angular Momentum. Problem 2 includes impulse, mass, and change in speed, so it would be solved using the Impulse-Momentum theorem.

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PRINCIPLE MATCH ONLY 09) Problem 1 (Newton’s Second Law with centripetal acceleration) FerrisWheel

Two friends with a combined mass of 130 kg share a seat on the Ferris wheel at a local carnival. The Ferris wheel has a diameter of 10 m and moves in a vertical circle at a constant speed of 0.5 m/s. What is the normal force that the seat exerts on the riders at the top of the circle?

Problem 2 (Newton’s Second Law with centripetal acceleration) DanglingKeys You are a passenger in a car rounding a turn with radius 150 m. You take out your keys from your pocket and dangle them from the end of your keychain. They make an angle of 20 degrees with the vertical, as shown in the diagram. What is the car’s speed?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include force, speed, and a circular path radius, so they would be solved using Newton’s Second Law with centripetal acceleration.

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10) Problem 1 (Newton’s Second Law with centripetal acceleration) ToyAirplane A 0.075 kg toy airplane is tied to the ceiling with a string. The motor makes the airplane move with a constant speed of 1.21 m/s in a horizontal circle of radius 0.44 m. Find the angle that the string makes with the vertical line shown in the diagram.

Problem 2 (Newton’s Second Law with linear acceleration) SpySafe A spy pushes on a 150-kg floor safe with a constant horizontal force, which causes the safe to accelerate at 0.05 m/s2. The coefficient of friction between the safe and the floor is 0.2. What is the magnitude of the spy’s push on the safe?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Problem 1 includes forces, speed and circular path radius, so it would be solved using Newton’s Second Law with centripetal acceleration. Problem 2 includes force and acceleration so it would also be solved by Newton’s Second Law.

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11) Problem 1 (Conservation of Energy) BowlingBall After you bowl a strike, your 7.25-kg bowling ball (radius 10.9 cm) rolls without slipping back toward the ball rack with a linear speed of 2.85 m/s. To reach the rack, the ball rolls up a ramp that gives the ball a 0.53-m vertical rise. What is the speed of the bowling ball when it reaches the top of the ramp?

Problem 2 (Conservation of Energy) GirlSwing Kelli weighs 420 N, and she is sitting on a playground swing seat that hangs 0.4 m above the ground. Tom pulls the swing back and releases it when the seat is 1.0 m above the ground. How fast is Kelli moving when the swing passes through its lowest position?

Feedback: (correct / incorrect). These problems would be solved similarly. Both problems include changes in height and speed, so they would be solved using Conservation of Energy.

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12) Problem 1 (Work-Energy Theorem) TowingCar A tow-truck uses a chain to pull a small car that is initially at rest. After a few seconds the small car is moving at speed 3 m/s. If the work done by the tow-truck on the car is 2250 Joules, what is the mass of the car?

Problem 2 (Work-Energy Theorem) Skier A skier with a mass of 40 kg travels down a frictionless hill that is 20-m high. The skier then encounters a rough patch of ground and is brought to rest after sliding for 48 m over the rough ground. How much work was done by the rough patch in bringing the skier to a stop?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include work and changes in speed, so they would be solved using the Work-Energy theorem.

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13) Problem 1 (Conservation of Momentum) AlphaParticle An alpha particle (mass 4.0 atomic mass units) collides with an oxygen nucleus (mass 16 amu) that is initially at rest. The alpha particle is scattered at an angle of 64 degrees from its initial direction of motion, and the oxygen nucleus recoils at an angle of 51 degrees on the opposite side of that initial direction at a speed of 1.20x105 m/s. What was the initial speed of the alpha particle?

Problem 2 (Conservation of Momentum) Squid A squid is able to propel itself forward by using a powerful muscle to squeeze water from its body cavity through a narrow opening at a high speed. If a 0.90-kg squid starts from rest and ejects 0.31 kg of water at a speed of 20 m/s, what is the resulting speed of the squid?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include mass and changes in speed with no external forces on the system, so they would be solved using Conservation of Momentum.

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14) Problem 1 (Impulse-Momentum Theorem) CrashDummy A car moving at 10 m/s crashes into a barrier and stops in 0.050 s. There is a 40-kg crash-test dummy in the car. Assume that the dummy’s velocity is changed by the same amount as the car’s in the same time period. What is the impulse on the dummy?

Problem 2 (Impulse-Momentum Theorem) Rocket Small rockets are used to make tiny adjustments in the speed of satellites. One such rocket provides a force of 35 N. What impulse is required to change the velocity of a 72,000 kg satellite by 63 cm/s?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include impulse, mass, and changes in speed, so they would be solved using the Impulse-Momentum theorem.

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15) Problem 1 (Conservation of Angular Momentum) CollapsingStar Suppose a star the size of our Sun (radius 6.96x108m), but 8.0 times as massive (1.59x1031kg), were rotating with an angular speed of 7.27x10-6 rad/s. If it were to undergo gravitational collapse to a neutron star of radius 10 km, losing ¾ of its mass in the process, what would its angular speed be?

Problem 2 (Conservation of Angular Momentum) ToyTrain A toy electric train with a mass of 8 kg is set up to run around a track of 0.75 m in radius on a freely rotating horizontal platform whose moment of inertia relative to the vertical axle at its center is 3 kg-m2. The train and platform are initially at rest. The train is then set in motion and its final angular speed relative to the ground is 2.7 rad/s, what is the angular speed of the platform relative to the ground?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include changes in angular speed with no external torque on the system, so they would be solved using Conservation of Angular Momentum.

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16) Problem 1 (Angular Impulse-Angular Momentum Theorem) EggBeater An angular impulse of 0.06 N∙m∙s is applied to an egg beater initially at rest. If the moment of inertia of the egg beater is 2.5 x 10-3 kg-m2, what is its angular speed?

Problem 2 (Angular Impulse-Angular Momentum Theorem) CelingFan A ceiling fan has three rod-like blades, each with a mass of 0.35 kg and a length of 60 cm. When the fan is turned on, it reaches an angular speed of 10 rad/s. Ignoring friction, what angular impulse was applied to the fan by the motor?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include angular impulse and changes in angular speed, so they would be solved using the Angular Impulse-Angular Momentum theorem.

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BOTH SURFACE & PRINCIPLE MATCH 17) Problem 1 (Newton’s Second Law) Suitcase01

A 60 kg woman pulls a 30 kg suitcase fitted with frictionless wheels along the ground by means of a strap. She pulls on the strap with 50 N at an angle of 40o above the horizontal, making the suitcase accelerate horizontally. Calculate the vertical force exerted by the ground on the suitcase.

Problem 2 (Newton’s Second Law) Suitcase02 A 10-kg suitcase initially at rest on the floor is lifted vertically a distance 0.30 m by an upward applied force of 140 N. What is the acceleration of the suitcase?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include forces and acceleration, so they would be solved using Newton’s Second Law.

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18) Problem 1 (Newton’s Second Law) TruckCrate01 A dump truck slowly tilts its bed upward to dispose of a 95.0-kg crate. For small angles of tilt, the crate stays put, but when the tilt angle exceeds 23.2o, the crate begins to slide. What is the coefficient of static friction between the bed of the truck and the crate?

Problem 2 (Newton’s Second Law with centripetal acceleration) TruckCrate02 A flatbed truck is carrying a heavy crate as it rounds a 25-m turn in the road. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum speed at which the driver can travel and still avoid having the crate slide?

Feedback: Correct / Incorrect. These problems would be solved similarly. Problem 1 includes force so it would be solved using Newton’s Second Law. Problem 2 includes force, speed, and circular path radius, so it would be solved using Newton’s Second Law with centripetal acceleration.

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19) Problem 1 (Conservation of Energy) Skateboarder01 A skateboarder enters a curved frictionless ramp moving horizontally with a speed of 6.5 m/s, and leaves the ramp moving vertically with a speed of 4.1 m/s. What is the height of the ramp?

Problem 2 (Conservation of Energy) Skateboarder02 A 60-kg skateboarder rolling along a horizontal region of frictionless pavement at a speed 3.0 m/s suddenly slides down a slope to a lower horizontal region. If the lower region is a distance 2.0 m below the top region, what is the speed of the skateboarder at the bottom?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include changes in height and speed, so they would be solved using Conservation of Energy.

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20) Problem 1 (Work-Energy Theorem) Slide01 A 30-kg girl climbs the 5-m high ladder of a playground slide. If she reaches a velocity of 3 m/s at the bottom of the slide, how much work was done by friction on the girl?

Problem 2 (Work-Energy Theorem) Slide02 A 30-kg trained seal slides from rest down a 3. 0-m-long ramp into a pool of water. The ramp is inclined at an angle of 23 degrees and friction does 240 J of work on the seal as it slides. What is the speed of the seal when it enters the water?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include work and changes in speed, so they would be solved using the Work-Energy theorem.

?

3 m

23o

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21) Problem 1 (Conservation of Momentum) CarCollision01 A 2500-kg truck traveling at 12 m/s collides, and becomes locked together, with a stationary 800-kg car. Determine the speed of the two vehicles immediately after the collision.

Problem 2 (Conservation of Momentum) CarCollision02 A 1000-kg car moving east at 17 m/s collides with a 1200-kg car moving south at 15 m/s and the two cars stick together. What is the speed and direction of the cars right after the collision?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include mass and change in speed with no external forces on the system, so they would be solved using Conservation of Momentum.

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22) Problem 1(Impulse-Momentum Theorem) Croquet A 0.50-kg croquet ball is initially at rest on the grass. The ball is struck by a mallet with a force of 230 N, giving it an impulse of 1.6 N-s. How fast does the ball move after being struck?

Problem 2 (Impulse-Momentum Theorem) SoccerKick A 0.25-kg soccer ball is rolling at 6.0 m/s toward a player. The player kicks the ball back in the opposite direction and gives it a velocity of 14 m/s. What was the impulse imparted to the ball by the player’s foot?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include impulse and change in speed, so they would be solved using the Impulse-Momentum theorem.

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23) Problem 1 (Conservation of Angular Momentum) RotatingDisk01 A 0.01-kg cockroach lies on the rim of a uniform 20-cm disk of mass 1.3 kg that can rotate freely about its center like a merry-go-round. Initially, the cockroach and disk rotate together at 2.2 rad/s. Then the cockroach walks halfway to the center of the disk. What is the final rotational speed of the cockroach-disk system?

Problem 2 (Conservation of Angular Momentum) RotatingDisk02 In the figure, the lower disk, of mass 440 g and radius 3.5 cm, is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.3 cm, is rotating in the opposite direction at 105 rpm. The top disk drops down the shaft onto the lower disk, and frictional forces act to bring the two disks to a common rotational speed. Find the final common rotational speed.

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include a change in rotational speed with no external torque on the system, so they would be solved using Conservation of Angular Momentum.

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24) Problem 1 (Angular Impulse – Angular Momentum Theorem) BilliardBall01 A billiard ball of radius 3 cm and mass 0.2 kg is given an impulse of magnitude 0.4 N·s when it is struck by a cue at a vertical distance of 1 cm from the top of the ball. If the ball rolls without slipping, find the final speed of the billiard ball.

Problem 2 (Angular Impulse – Angular Momentum Theorem) BilliardBall02 A fixed cylinder (mass 2 kg, radius 0.6 m) is free to rotate about an axle through its center. The cylinder is given an impulse 5 N·s, by a force applied at a distance 0.4 m from the center. If the cylinder is initially at rest, what is the angular speed of the cylinder about its center of mass after the impulse is delivered?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include an angular impulse and changes in angular speed, so they would be solved using the Angular Impulse – Angular Momentum theorem.

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NEITHER SURFACE NOR PRINCIPLE MATCH 25) Problem 1 (Newton’s Second Law) WaterPail

Jack and Jill lift upward on a 1.3-kg pail of water, with Jack pulling at 7.0 N and Jill pulling at 11 N at an angle of 28 degrees with the vertical. At what angle with respect to the vertical should Jack lift on the pail is to accelerate straight upward?

Problem 2 (Work-Energy Theorem) PullingSled A sled of mass 50 kg is on frictionless snow. A child pulls on the sled with a force of 11.0 N at an angle of 20° above the horizontal, doing 21 J of work on the sled. If the sled starts from rest, what is the final speed of the sled?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes forces and acceleration so it would be solved using Newton’s Second Law. Problem 2 includes work and change in speed so it would be solved using the Work-Energy theorem.

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26) Problem 1 (Conservation of Energy) ArcherFish The archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish’s mouth. Suppose the archerfish squirts water with an initial speed of 2.3 m/s at a beetle on a leaf 3.0 cm above the water’s surface. With what speed does the water hit the beetle?

Problem 2 (Impulse-Momentum Theorem) Golfer A golfer hits a golf ball, giving it an initial speed of 50 m/s directed 50o above the horizontal. Assuming that the mass of the ball is 46 g and the club and ball are in contact for 1.7 ms, find the impulse on the ball.

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes changes in height and speed, so it would be solved using Conservation of Energy. Problem 2 includes impulse, mass and change in speed so it would be solved using the Impulse-Momentum theorem.

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27) Problem 1 (Angular Impulse – Angular Momentum Theorem) RotatingDiver During the launch from a board, a diver’s rotational speed about his center of mass changed from zero to 6.20 rad/s. His rotational inertia about his center of mass was 12.0 kg-m2. What was the angular impulse on him from the board?

Problem 2 (Work-Energy Theorem) TireRotate A truck mechanic gives a large truck tire a hard shove doing 300 J of work on it. The tire then rolls without slipping along a level concrete driveway. If we treat the truck tire as a disk of mass 40 kg and radius 0.5 m, what is the speed of the tire?

Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes angular impulse and changes in rotational speed so it would be solved using the Angular Impulse – Angular Momentum theorem. Problem 1 includes work and change in speed so it would be solved using the Work-Energy theorem with rotational energy.

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28) Problem 1 (Conservation of Momentum) AstronautWrench An astronaut in space initially at rest is holding a 1-kg wrench in her hand. The mass of the astronaut (including her space suit) is 90 kg. The astronaut then throws the wrench into space. Onlookers in the space shuttle see the wrench moving with a speed of 5 m/s. How fast is the astronaut moving after throwing the wrench?

Problem 2 (Angular Impulse-Angular Momentum Theorem) RodImpulse A uniform rod of mass 8.4 kg and length 1.3 m is pivoted at one end and hangs vertically. It is struck by a bat (swung horizontally) that delivers an angular impulse 7.4 N·m·s to the rod perpendicular to its rotational axis. What is the angular speed of the rod just after it is struck?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes mass and change in speed with no external forces on the system, so it would be solved using Conservation of Momentum. Problem 2 includes angular impulse and change in angular speed, so it would be solved using the Angular Impulse-Angular Momentum theorem.

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29) Problem 1 (Conservation of Angular Momentum) TwoSkaters Two equal mass ice skaters are holding hands with arms outstretched and spinning at 3 rad/s while facing each other. They then pull their arms in tight, and spin at the higher rate of 6.3 rad/s. By what factor was the moment of inertia reduced when they pulled in their arms?

Problem 2 (Newton’s second law with centripetal acceleration) CarBanked A 900 kg compact car is traveling around a circular banked track at a constant speed of 20.5 m/s. The radius of the circular track is 85 m. Find the appropriate angle such that the car can round the curved track without slipping and without any assistance from friction between the tires and the road.

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes a change in angular speed with no external torque on the system, so it would be solved using Conservation of Angular Momentum. Problem 2 includes forces, speed, and circular path radius, so it would be solved using Newton’s second law with centripetal acceleration.

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30) Problem 1 (Conservation of Momentum) Toboggan A runaway toboggan of mass 8.6 kg sliding over a horizontal snow region at 23 km/h passes under a tree. At that instant, a 15 kg clump of snow falls into the toboggan. What is the subsequent speed of the toboggan?

Problem 2 (Newton’s second law) GroceryBag Your groceries are in a bag with paper handles. The handles will tear off if a force greater than 52 N is applied to them. What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised with an acceleration of 1.32 m/s2?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes mass and change in speed with no external forces on the system, so it would be solved using Conservation of Momentum. Problem 2 includes forces and acceleration, so it would be solved using Newton’s Second Law.

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31) Problem 1 (Angular Impulse-Angular Momentum Theorem) SandingDisk A sanding disk with rotational inertia 1.2x10-3 kg-m2 is attached to an electric drill whose motor delivers an angular impulse of 5.3x10-4 N-m-s. What is the angular speed of the disk after the motor is turned on?

Problem 2 (Newton’s 2nd Law with centripetal acceleration) MerryGoRound01 A child sits on a rotating merry-go-round, 2.1 meters from its center. If the speed of the child is 1.9 m/s, what is the minimum coefficient of static friction between the child and the merry-go-round that will prevent the child from slipping?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes angular impulse and change in angular speed, so it would be solved using the Angular Impulse – Angular Momentum theorem. Problem 2 includes force, speed, and circular path radius, so it would be solved using Newton’s Second Law with centripetal acceleration.

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32) Problem 1 (Conservation of Angular Momentum) IceSkater A 60-kg ice skater is initially spinning at a rate of 10.0 rad/s with a rotational inertia of 2.50 kg-m2 when her arms are extended. What is her angular speed after she pulls her arms in and reduces her rotational inertia to 1.60 kg-m2?

Problem 2 (Impulse-Momentum Theorem) Archer An archer shoots a 0.01-kg arrow at a stationary target with a speed of 43 m/s. When it hits the target, it penetrates to a depth of 0.05 m and comes to a stop. What was the impulse on the arrow?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes change in angular speed with no external torque on the system, so it would be solved using Conservation of Angular Momentum. Problem 2 includes impulse and change in speed, so it would be solved using the Impulse-Momentum theorem.

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INITIAL REASONING SLIDES Surface Match 33) Problem 1 (Newton’s Second Law) Elevator01

An elevator of mass 1000 kg accelerates downward at 3.2 m/s2. Find the tension in the cable.

Problem 2 (Conservation of Energy or Kinematics) Elevator02 An elevator is initially at rest, held by a cable. The cable then snaps and the elevator falls downward. After the elevator has fallen 20 meters, how fast is it moving?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes force and acceleration, so it would be solved using Newton’s Second Law. Problem 2 includes changes in height and speed, so it would be solved using Conservation of Energy.

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34) Problem 1 (Conservation of Energy) BaseballThrow A baseball (mass of 0.15 kg) is thrown by a little-league player from center field to second base. The ball reaches a maximum height of 4 m above the point from which the player threw it and was traveling at 6 m/s at that point. What was the initial speed of the ball?

Problem 2 (Impulse-Momentum Theorem) Catcher A catcher stops a 92 mi/h (41 m/s) pitch in his glove, bringing it to rest in 0.007 seconds. If the impulse on the ball by the catcher is 5.9 N-s, what is the mass of the ball?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes changes in height and speed, so it would be solved using Conservation of Energy. Problem 2 includes impulse and changes in speed, so it would be solved using the Impulse-Momentum theorem.

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Neither Surface nor Principle Match 35) Problem 1 (Conservation of Energy) RescueNet

A 70-kg man steps out of a window and lands in an elevated fire rescue net 5.0 m below the window. He momentarily stops when the net is stretched vertically by 1.5 m. What is the spring constant of the net?

Problem 2 (Conservation of Angular Momentum) MerryGoRound02 A small playground merry-go-round has radius 3.5 meters and moment of inertia 1300 kg·m2. With her child sitting on the edge, a parent pushes the merry-go-round until the angular speed is 3 rad/s. What is the angular speed if the child (mass 40 kg) moves to a distance 1 m from the center?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes changes in height and spring stretch, so it would be solved using Conservation of Energy. Problem 2 includes changes in angular speed with no external torque on the system, so it would be solved using Conservation of Angular Momentum.

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Neither Surface nor Principle Match 36) Problem 1 (Impulse-Momentum Theorem) Icicle

An icicle of mass 10 g falls vertically from a roof and hits a very thick layer of snow. The snow does 0.2 J of work in bringing the icicle to rest. Find the speed of the icicle just prior to hitting the snow.

Problem 2 (Newton’s second law with centripetal acceleration) FuzzyDice A pair of fuzzy dice is hanging by a string from a rearview mirror of a car. If the car rounds a curve with a radius of 25 m at a speed of 10 m/s, what angle does the string make with the vertical?

Feedback: Correct / Incorrect. The problems would NOT be solved similarly. Problem 1 includes work and changes in speed so it would be solved using the Work-Energy theorem. Problem 2 includes forces, speed and circular path radius, so it would be solved using Newton’s Second Law with centripetal acceleration.

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Principle Only Match 37) Problem 1 (Conservation of Momentum) Explosion

A 16-kg object with speed 800 m/s explodes into two pieces, one 4 kg and the other 12 kg. The explosion takes place in gravity-free space. The less massive piece is observed to be at rest just after the explosion. What is the speed of the larger piece after the explosion?

Problem 2 (Conservation of Momentum) CoalTrain A 5800-kg open railroad car coasts along with a constant speed of 1.5 m/s on a level track. Coal falls vertically from a chute and fills the car at a rate of 100 kg/sec. Ignoring friction with the tracks, what is the speed of the train car after 20 seconds?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include changes in mass and speed with no external forces on the system, so they would be solved using Conservation of Momentum.

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Principle Only Match 38) Problem 1 (Impulse-Momentum Theorem) HitBall

A 0.14-kg baseball moves horizontally with a speed of 35 m/s toward a bat. After striking the bat the ball moves vertically upward with half its initial speed. Find the direction and magnitude of the impulse delivered to the ball by the bat.

Problem 2 (Impulse-Momentum Theorem) HeartMuscle According to a simplified model of a mammalian heart, at each pulse, approximately 20 g of blood is accelerated from by a force of 0.02 N during a period of 0.10 s. What is the change in the blood’s momentum?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include impulse and changes in speed, so they would be solved using the Impulse-Momentum theorem.

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Both Principle and Surface Match 39) Problem 1 (Conservation of Energy) RollerCoaster01

A 200-kg roller coaster car with an initial speed of 15 m/s slides down a hill of height 8 m, then up a second hill of height 15 m. Assume the track is frictionless. What is the speed of the car at the top of the 15 meter hill?

Problem 2 (Conservation of Energy) RollerCoaster02 A 150-kg roller coaster car has an initial speed of 3 m/s at height 20 m from the bottom of a loop-the-loop as shown. The radius of the circle is 4 m. Assume the track is frictionless. What is the speed of the car at the top of the circular loop?


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Both Surface and Principle Match 40) Problem 1 (Newton’s second law with centripetal acceleration) CarCurve01

Driving in your car, you encounter a small hill in the road that has a circular cross section of radius 35 m. At what speed must you go over the bump if people in your car are to feel “weightless”?

Problem 2 (Newton’s second law with centripetal acceleration) CarCurve02 A 1000-kg car rounds a curve on a flat road of radius 50 m at a speed of 14 m/s. Will the car make the turn, or will it skid, if the pavement is icy and the coefficient of static friction is 0.25?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include force, speed, and circular path radius, so they would be solved using Newton’s Second Law with centripetal acceleration.

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FINAL REASONING SLIDES Surface Only Match 41) Problem 1 (Conservation of Momentum - Linear) PuttyRod01

A rod of length 1 m and mass 0.6 kg is initially at rest on a very slippery horizontal surface. A chunk of putty of mass 0.1 kg sliding on the surface at 2.7 m/s perpendicular to the rod hits and sticks to the rod 0.25 m from one end, as shown. What is the final speed of the center of mass of the putty-rod system after the collision?

Problem 2 (Conservation of Angular Momentum) PuttyRod02 A rod of length 1 m and mass 0.6 kg is initially at rest on a very slippery horizontal surface. A chunk of putty of mass 0.1 kg sliding on the surface at 2.7 m/s perpendicular to the rod hits and sticks to the rod 0.25 m from one end, as shown. What is the final angular speed about the center of mass of the putty-rod system after the collision?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes changes in linear speed with no external forces on the system, so it would be solved using Conservation of Momentum. Problem 2 includes changes in angular speed with no external torque on the system, so it would be solved using Conservation of Angular Momentum.

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Surface Only Match 42) Problem 1 (Impulse-Momentum Theorem) HockeyPuck01

A hockey puck has a mass of 0.12 kg and is at rest. A hockey player makes a shot, giving the puck an impulse of 480 N-s. With what speed does it head toward the goal?

Problem 2 (Newton’s Second Law) HockeyPuck02 A hockey player uses his stick to push on a 0.12-kg puck with a force of 0.35 N and skates toward the goal with a constant velocity of 2 m/s. What is the coefficient of kinetic friction between the puck and the ice?

Feedback: (Correct / Incorrect). These problems would NOT be solved similarly. Problem 1 includes impulse, mass, and change in speed so it would be solved using the Impulse-Momentum Theorem. Problem 2 includes balanced forces with no acceleration so it would be solved using Newton’s Second Law.

Principle Only Match 43) Problem 1 (Newton’s Second Law) Parachute

A sky diver of mass 70 kg (including parachute) falls freely for 50 meters. After releasing the parachute, the diver descends leisurely to the ground at a constant speed. What was the force due to air resistance on the sky diver when the parachute was open?

Problem 1 (Newton’s Second Law) HangingSign A 20-kg sign is supported by two ropes that are at an angle of 20o to the horizontal. What is the tension in the ropes?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include balanced forces with no acceleration so they would be solved using Newton’s Second Law.

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Principle Only Match 44) Problem 1 (Work-Energy Theorem) Shuffleboard

In a shuffleboard game, a 0.5-kg disk is pushed by a stick and given an initial speed of 2 m/s. It slides a distance 8 m before coming to rest. How much work was done by friction in bringing the disk to rest?

Problem 2 (Work-Energy Theorem) DragRacer A drag racer crosses the finish line traveling at 200 km/h, and promptly deploys her drag chute (the small parachute used for braking). The parachute does 1300 kJ of work in slowing the car to 30 km/h. What is the mass of the car?

Feedback: (Correct / Incorrect). These problems would be solved similarly. Both problems include work and changes in speed, so they would be solved using the Work-Energy theorem.

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Both Surface and Principle Match 45) Problem 1 (Conservation of Angular Momentum) PuckTable01

A small 0.1-kg puck is attached to a light string which passes through a hole in the middle of a horizontal frictionless table. The puck is set into rotation in a circle of radius 1.2 m with a speed 3 rad/s. The string is then pulled down, shortening the path to 0.7 m. What is the new angular speed of the puck as it travels in a circle?

Problem 2 (Conservation of Angular Momentum) PuckTable02 An 88-g puck is tied to the end of a string of length 150 cm. The other end of the string is tied to the center of an air table, and the puck is given a shove so that it moves in a circle at angular speed 0.75 rad/s. A 12-g piece of clay is dropped onto the puck and sticks to it. What is the final angular speed of the puck-clay system as the two continue to move in a circle?

Feedback: Correct / Incorrect. These problems would be solved similarly. Both problems include change in angular speed with no external torque on the system, so they would be solved using Conservation of Angular Momentum.

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Both Principle and Surface Match 46) Problem 1 (Conservation of Energy) SwingingBoy

A 40-kg boy swings on a lightweight rope attached to a tree near his favorite swimming hole. At the bottom of the rope’s swing, the boy is just above the water and has a speed of 6 m/s. What was the initial height of the boy above the water?

Problem 2 (Conservation of Energy) SwingingMonkey A monkey is trying to reach a banana that is hanging 3.0 m above the ground from a tree. The monkey runs towards a vine, grabs it, and then swings on the vine up to the banana. How fast does the monkey need to run just prior to grabbing the vine in order to reach the banana?


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Neither Surface nor Principle Match 47) Problem 1 (Work-Energy Theorem) PoleVaulter

A pole vaulter of mass 70.0 kg vaults to a height of 6.0 m before dropping to thick padding placed below to cushion his fall. He lands with a speed of 2.5 m/s and comes to a stop after 10 cm. How much work was done by the padding on the vaulter?

Problem 2 (Impulse-Momentum Theorem) HitBall01 A tennis ball may leave the racket of a top player on the serve with a speed of 65 m/s. Assume the ball starts at rest with respect to the tennis racket. If the impulse delivered to the ball by the racket is 3.9 N-s, what is the mass of the ball?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes work and change in speed, so it would be solved using the Work-Energy theorem. Problem 2 includes impulse and change in speed, so it would be solved using the Impulse-Momentum theorem.

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Neither Surface nor Principle Match 48) Problem 1 (Impulse-Momentum Theorem) SkaterLeap

A 60-kg ice skater jumps into the air and lands from the leap with a speed of 2.5 m/s. As she lands, her knees bend, lengthening the stopping time to 0.05 seconds. Find the impulse on the skater’s body.

Problem 2 (Conservation of Energy) DartGun A dart of mass 0.100 kg is pressed against the spring of a toy dart gun. The spring (with spring constant 250 N/m) is compressed 6.0 cm and released. What speed does the dart acquire?

Feedback: Correct / Incorrect. These problems would NOT be solved similarly. Problem 1 includes impulse and changes in speed, so it would be solved using the Impulse-Momentum theorem. Problem 2 includes changes in speed and spring compression, so it would be solved using Conservation of Energy.

1 auxiliary appendix: instructions and items a

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