forces inertia, mass, weight newton’s law types of forces free-body diagram friction

FORCES Inertia, Mass, WeightNewton’s LawTypes of ForcesFree-body diagramFriction

FORCE Push/pull Causes an object to accelerate or change its

velocity. Net force: sum of all forces Two types of forces:

a) Contact forcesb) Field forces

• Gravitational …objects• Electromagnetic…Charges• Nuclear…subatomic particle• Weak…radioactive decay

Vector

Inertia, Mass, and Weight Inertia

Resistance to change in its state of motion

Depends on mass Example

• Pushing heavy things• When moving…difficult to stop• Seatbelts

Galileo and inertia• Incline plane: initial height = final height

Inertia, Mass, and Weight Mass

Amount of matter it has Measures inertia Units: kg Remains constant

Weight Changes with gravity Measures force Units: Newton

Inertia, Mass, and Weight Examples Mac and Tosh are arguing in the cafeteria. Mac says that if he

throws his jello with a greater speed it will have a greater inertia. Tosh argues that inertia does not depend upon speed, but rather upon mass. With whom do you agree? Why?

If you were in a weightless environment in space, would it require a force to set an object in motion?

Mr. Wegley spends most Sunday afternoons at rest on the sofa, watching pro football games and consuming large quantities of food. What effect (if any) does this practice have upon his inertia? Explain.

Ben Tooclose is being chased through the woods by a bull moose which he was attempting to photograph. The enormous mass of the bull moose is extremely intimidating. Yet, if Ben makes a zigzag pattern through the woods, he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton's first law of motion.

Newton’s First Law Law of inertia Two parts

Object at rest, remains at rest Object in motion, remains in motion Unless an unbalance force acts

upon it No force needed to keep an object in

motion Resists acceleration

Newton’s First Law

Contradicted: Aristotle: all objects have natural tendency come to rest

Newton: all objects come to rest due to friction; w/o friction object continues to move

Balanced and unbalanced forces


http://www.physicsclassroom.com/Class/newtlaws/U2L1a.html

Newton’s Second Law• A net force or unbalanced forces

causes an object to accelerate in the direction of the force.

• Acceleration is directly proportional to the force

Newton’s Second Law• Acceleration is inversely proportional to

the mass

• Fnet = ma• Units: Newton (N) = kg·m / s2

• Vector sum of all forces• FORCES CAUSE ACCELERATION!!

Newton’s Second LawEquilibrium means “Zero” acceleration

Newton’s Second Law Free Fall All objects will fall with the same

rate of acceleration, regardless of their mass

Air Resistance Decreases the acceleration Depends on cross-sectional area and

speed Terminal Velocity

Weight equals force due to air resistance; a = 0 m/s/s

Newton’s Second Law

NEWTON’S SECOND LAW

Problems: Pg 92 1) When a shot-putter exerts a net force of

140 N on a shot, the shot has an acceleration of 19 m/s/s. What is the mass of the shot?

7.4 kg 2) Together a motorbike and rider have a

mass of 275 kg. The motorbike is slowed down with an acceleration of –4.50 m/s/s. What is the net force on the motorbike? Describe the direction of this force and the meaning of the negative sign.

- 1.24 x 103 N; direction of force is in opposite direction of the velocity.

Problems: Pg 92 3) A car, mass 1225 kg, traveling at 105

km/h, slows to a stop in 53 m. What is the size and direction of the force that acted on the car? What provided the force?

- 9.8 x 103 N; road surface pushing against the car tires

4) Imagine a spider with mass 7.0 x 10-5 kg moving downward on its thread. The thread exerts a force that results in a net upward force on the spider of 1.2 x 10-4 N.a) What is the acceleration of the spider?b) Explain the sign of the velocity and describe in words how the thread changes the velocity of the spider.

1.7 m/s/s

Newton’s Third Law

Two different objects Action-reaction pair For every action force there is a

equal and opposite reaction force F object A on object B = - F object B on object A

Newton’s Third Law

Types of Forces Applied Force (FA)

Applied to an object by another object Force of Gravity (Fg or W)

W = mg Perpendicular to the Earth

Normal or Support Force (Fn or N) Exerted by contact with a surface Perpendicular to the surface

Tension (T) Force exerted by strings, ropes, and wires

Spring Force (Fs) Force exerted by compressed or stretch spring

Friction Force (Ff) Opposes motion of object

FRICTIONAL FORCE Fluids or surface drag Opposes motion Two types:

Static friction…friction at rest• Ff sFn

• Maximum value Kinetic/sliding friction…friction in motion

• Ff = kFn

FRICTIONAL FORCE Coefficient of static friction ()

Measures how difficult it is to slide one material over another.

Dimensionless Independent

• surface area• speed (except when v =0)• temperature• roughness/texture

Dependent • nature of the surfaces (material)

Proportional to normal force k < s

FRICTIONAL FORCE

FREE-BODY DIAGRAM Diagrams showing all forces that are

found on the object with direction and magnitude

Arrows start from the center of the object.

Each arrow is labeled.

FREE-BODY DIAGRAM EXAMPLES The force of gravity on a wagon is 230 N. The force

of friction between the tires and the ground is 10 N. Sheila is pulling the wagon with a force 15 N. Draw the free body diagram showing the forces on the wagon.

A book is at rest on a table top. A girl is suspended motionless from a bar which

hangs from the ceiling by two ropes. An egg is free-falling from a nest in a tree. Neglect

air resistance. A flying squirrel is gliding (no wing flaps) from a tree

to the ground at constant velocity. Consider air resistance.

FREE-BODY DIAGRAM EXAMPLES A rightward force is applied to a book in order to

move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance.

A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance.

A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder.

A skydiver is descending with a constant velocity. Consider air resistance.

A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration.

FREE-BODY DIAGRAM EXAMPLES

A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance.

A car is coasting to the right and slowing down.

FREE-BODY DIAGRAM Write a Fnet equation

Fx and Fy equations. Fnet = ma Balanced Forces

At rest Constant velocity…a = 0 m/s/s Fnet = ma = 0

Unbalanced Forces a 0 Fnet = ma

Free Body Diagrams Calculations

Fx = Fa – Ff = ma Fy = Fn – Fg = ma


Fx = Ff = ma Fy = Fn – Fg = ma


Fx = Fa - Ff = ma Fy = Fn – Fg = ma


Fy = A – Fg = ma = 0


Fx = Fa - A = ma Fy = Fn – B = ma

Problems: Pg 94 5) What is the weight of each of the

following objects?a) 0.113 kg hockey puckb) 108 kg football playerc) 870kg automobile

1.11 N; 1.06 x 103 N; 8.50 x 103N 6) Find the mass of each of these

weights.a) 98 N b) 80 N c) 0.98 N

10 kg; 8.2 kg; 0.10 kg

Problems: Pg 94 7) A 20 N stone rests on a table. What is

the force the table exerts on the stone? In what direction?

20 N, upward 8) An astronaut with mass 75 kg travels to

Mars. What is his weighta) on Earthb) What is the weight on Mars where g = 3.8 m/s/s?

c) What is the value of g on top of a mountain if the astronaut weight 683 N?

740 N; 290 N; 9.1 m/s/s

Problems: Pg 99 9) Suppose Joe, who weighs 625 N, stands on a

bathroom scale calibrated in Newton.a) What force would the scale exert on Joe? In what direction?b) If Joe now holds a 50 N cat in his arms, what force would the scale exert on him?c) After Joe puts down the cat, his father comes up behind him and lifts upward on his elbows with a 72 N force. What force does the scale now exert on Joe?

625 N, upward; 675 N; 553 N upward 10) A 52 N sled is pulled across a cement sidewalk

at constant speed. A horizontal force of 36 N is exerted. What is the coefficient of sliding friction between the sidewalk and the metal runners of the sled?

0.69

Problems: Pg 100 10b) Suppose the sled now runs on packed

snow. The coefficient of friction is now only 0.12. If a person weighing 650 N sits on the sled, what force is needed to slide the sled across the snow at constant speed?

84 N 11) The coefficient of sliding friction

between rubber tires and wet pavement is 0.50. The brakes are applied to a 750 kg car traveling 30 m/s, and the car skids to a stop.a) What is the size and direction of the force of friction that the road exerts on the car?

-3.7 x 103 N

Problems: Pg 100 11b) What would be the size and direction of

the acceleration of the car? Why would it be constant?c) How far would the car travel before stopping?

-4.9 m/s/s; frictional force is constant; 92 m 12) If the tires of the car in Practice Problem

11 did not skid, the coefficient of friction would have been 0.70. Would the force of friction have been larger, smaller, or the same? Would the car have come to a stop in a shorter, the same, or a longer distance?

Larger; shorter distance

Problems: Pg 102 13) A rubber ball weighs 49 N.

a) What is the mass of the ball?b) What is the acceleration of he ball if an upward force of 69 N is applied?

5.0 kg; 4.0 m/s/s 14) A small weather rocket weighs 14.7 N.

a) What is its mass?b) The rocket is carried up by a balloon. The rocket is released from the balloon and fired, but its engine exerts an upward force of 10.2 N. What is the acceleration of the rocket?

1.5 kg; -3.00 m/s/s

Problems: Pg 102 15) The space shuttle has a mass of 2.0 x

106 kg. At lift-off the engines generate an upward force of 30 x 106 N.a) What is the weight of the shuttle?b) What is the acceleration of the shuttle when launched?c) The average acceleration of the shuttle during its 10 minute launch is 13 m/s/s. What velocity does it attain?d) As the space shuttle engines burn, the mass of the fuel becomes the same, would you expect the acceleration to increase, decrease or remain the same? Why?

2 x 107 N; 5.0 m/s/s; 7.8 km/s; increase

Problems: Pg 102 16) A certain sports car accelerates

from 0 to 60 mph in 9.0 s (average acceleration = 3.0 m/s/s). The mass of the car is 1354 kg. The average backward force due to air drag during acceleration is 280 N. Find the forward force required to give the car this acceleration.

4.4 x 103 N

Free Body Diagrams Calculations A rightward force is applied to a 6-kg object to

move it across a rough surface at constant velocity. The object encounters 15 N of frictional force. Use the diagram to determine the gravitational force, normal force, net force, and applied force. (Neglect air resistance.)

A rightward force is applied to a 10-kg object to move it across a rough surface at constant velocity. The coefficient of friction, µ, between the object and the surface is 0.2. Use the diagram to determine the gravitational force, normal force, applied force, frictional force, and net force.


A force of 55 N[E] acts on a combination of two boxes that are next to each other on a frictionless surface. Find:

a. the acceleration of the boxes. b. the force exerted by box A on box B. c. the force exerted by box B on box A.

Free Body Diagrams CalculationsThree toboggans are connected by a rope. The first

toboggan has a mass of 75 kg, the second a mass of 55 kg and the third a mass of 10 kg. If the force exerted on the first toboggan is 310 N and surfaces are considered to be frictionless. Find:

a. the acceleration of the toboggans b. the force exerted by toboggan one on toboggan two. c. the force exerted by toboggan two on toboggan

three.

NEXT-TIME QUESTION

As she falls faster and faster through the air, her acceleration

a) increasesb) decreasesc) remains the same

NEXT-TIME QUESTIONb) decreases

Acceleration decreases because the net force on her decreases. Net force is equal to her weight minus her air resistance, and since air resistance increases with increasing speed, net force and hence acceleration decrease. By Newton's 2nd law:

where mg is her weight, and R is the air resistance she encounters. As R increases, a decreases. Note that if she falls fast enough so that R = mg, a = 0, then with no acceleration she falls at constant velocity.

NEXT-TIME QUESTIONIf an elephant and a feather fall from a high

tree, which one will encounter the greater force of air resistance while falling to the ground below?

NEXT-TIME QUESTIONthe elephant

A much greater force of air resistance acts on the elephant simple because it has to "plow through" more air to get to the ground. So air resistance is greater on the elephant. The effect of air resistance is more pronounced for the feather, however, because air resistance doesn't have to build up very much to counteract the weight of the feather. A tiny fraction of one Newton of air resistance acting on a feather that weighs a tiny fraction of one Newton, more easily produces a zero net force and zero acceleration, compared to several Newtons of air resistance acting on thousands of Newtons of elephant. Remember to distinguish between a force itself and the effect it produces!

NEXT-TIME QUESTION

For every force there exists an equal and opposite force. Consider action and reaction forces in the case of a rock falling under the influence of gravity. If action is considered to be that of the Earth pulling down on the rock, can you clearly identify the reaction force?

NEXT-TIME QUESTIONreaction: the falling rock pulling up on the Earth

The recipe for action-reaction forces is simple enough: if A exerts force on B, then in turn; B exerts force on A. So if action is the earth pulling down on the falling rock, reaction is simply the falling rock pulling up on the Earth. Does this mean that the acceleration of the rock and the Earth should be the same? Not at all, but only because the Earth's mass is so much greater than that of the falling rock.

NEXT-TIME QUESTIONTwo smooth balls of

exactly the same size, one made of wood and the other of iron, are dropped from a high building to the ground below. The ball to encounter the greater force of air resistance on the way down is the a) wooden ball b) iron ball c) both the same

NEXT-TIME QUESTIONb) iron ballAir resistance depends on both the size and speed

of a falling object. Both balls have the same size, but the heavier iron ball falls faster through the air and encounters more air resistance in its fall.

NEXT-TIME QUESTIONShe holds the book

stationary against the wall as shown. Friction on the book by the wall acts

a) upward. b) downward. c) can't say

NEXT-TIME QUESTIONc - we can't say unless we know how the

vertical component of her push compares with the weight of the book, we can't specify the direction of friction between the book and the wall.

This defense-minded episode concerns Dr. J's dual role as a physics teacher and a part-time CIA agent. The United States (represented by Dr. J) and Russia were both working on a real-life nuclear-powered limb (á la Steve Austin) to be used by government spies who might have lost or damaged their arms in some way. (You guessed it - this is the famous nuclear arms race.) Finally, both countries finished limbs and fitted them to suitable subjects. The Russians tested theirs by having their agent (Big Fist) throw a ball weighing 490 N straight up into the air. They measured the initial acceleration of the ball to be 100 m/sec2. Dr. J decided to test his limb in a different manner. He had his agent push a large safe across the street. In order to push the safe (which weighed 5000 N), he had to overcome a force of friction of 3500 N. In addition, members of SAP (being against any type of physics) decided to push against the safe opposite to the bionic subject with a force of 500 N. The bionic subject still managed to accelerate the safe forward.

At what minimum rate would the safe have to accelerate in order to demonstrate a superior American force?

a > 2.92 m/s2

The Russian force (FR) would be the sum of the net force required to accelerate the ball plus the weight of the ball. The mass of the ball can be found by the fact that: Fw = mag

The net force is found by: Fnet = ma Fnet = (50 kg) (100 m/s) Fnet = 5000 N

Therefore: FR = 5000 N + 490 N FR = 5490 N

The American force, FA, must exceed, however slightly, 5490 N. The acceleration produced by an American force of 5490 N is found as follows: The mass of the safe is found by:

.

The net force is equal to the American force minus the two opposing forces provided by friction and the members of SAP.

Fnet = 5490 N - (3500 N + 500 N) Fnet = 1490 N

The acceleration is then found by:

The minimum rate must exceed this value: a > 2.92 m/s2

This is the sad story of a lover's leap foiled by the fate of physics. The romance centers around Dr. J's maiden aunt and her so-called boyfriend, Jilting Joe from Buffalo. Aunt J and Jilting Joe had only known each other for a few weeks, but she was sure it was a Coca-Cola relationship (the real thing). On the other hand, Dr. J viewed it as a sour-milk setup (it smelled from the very beginning). When Jilting Joe proposed marriage, Dr. J feared that he was after her bank account more than her homely face and lack of grace. Therefore, in final desperation, Dr. J locked his aunt in her second- story bedroom. Not to be stopped, Jilting Joe established communication with Aunt J by sending sines through the window with a flashlight (this guy knew all the angles). She responded with matching sines (that's right-cosines). Together they decided on a final plan - they would elope (check the title). Jilting Joe signaled for Aunt J to make a rope out of hosiery and slide down to his waiting arms. She couldn't decide which brand to use - Leggs, since they were running away, or No-Nonsense, since this was nothing to fool around about. She finally decided that Jilting Joe would prefer Hanes (although we know better). As luck would have it, she came down too slowly, causing the hosiery rope to break. In the resulting fall, she fell head over heels for Jilting Joe. However, it proved to be the final blow to their relationship, as Joe failed to survive.

If Aunt J weighed 750 N, and if the hosiery rope could only withstand a maximum tension of 600 N, what was the minimum acceleration that Aunt J could have had in order not to break the rope?

1.96 m/sec2

Aunt J's mass can be determined from her weight by:

If the force of gravity on Aunt J was 750 N downward and the force of the rope (tension) exerted on Aunt J was 600 N upward, the net force exerted on Aunt J was 150 N downward. The resulting acceleration is then found by:

Dr. J is working hard to make Labor Day a memorable holiday for all of his relatives. It is his turn to host the annual family reunion, and he has decided to have a picnic in the park. He is especially interested in providing a good time for all of his nieces and nephews. To insure this, he assigns someone to be in charge of each area. For example, Tripod will help with the three-legged race, while Dr. J's henpecked brother-in-law will barbecue the chicken. Uncle Darwin will supervise play on the monkey bars while his thrice-divorced sister is a natural choice for the merry-go-round. His uncle, a retired carpenter who made a fortune building shorefront condominiums, will manage the see-saws, while a playboy cousin will watch the swingers. That only leaves the sliding board, which Dr. J eagerly assigns to himself. As he once said, "Isn't it just great to watch kids accelerate?“

If the sliding board makes an angle of 60º with the ground and the coefficient of sliding friction between the kids and the sliding board is 0.15, at what rate will they accelerate?

7.75 m/sec2

The weight of the children, Fw, does not affect the rate of acceleration. The components of the weight are found by:

The force of friction, FF, is found using the coefficient of friction:

The net force down the slide is equal to the difference between the component parallel to the slide, FP and friction:

The mass of the children can be found using their weight:

The acceleration is determined using Newton's Second Law:

Dr. J was so displeased with his season tickets for local football games that he invented his own version of a box seat. It was designed to let Dr. J and his dog Tripod view the games from a different angle. One night, while watching a game from his favorite angle of 25º, Dr. J, Tripod, and the box seat were taken for a ride. A former member of SAP named Cy had left the organization in order to have himself cloned nine times. He and his clones had formed a new group. (Yes, the Cyclones - I hope I didn't blow you away with that one.) Cy attached a rope of negligible weight to the back of the box and then ran it up the incline and over a frictionless pulley. Cy and the Cyclones were then able to climb into an attached 50 N box, causing Dr. J, Tripod, and the box seat to accelerate up the incline at a rate of 8.00 m/sec2.

If the box seat and its contents weighed 1000 N, and the coefficient of kinetic friction was 0.466, how much did Cy weigh?

899 N

The problem involves no less than five simultaneous forces. Dr. J's box and contents exert a force normal to the plane, FN, and parallel to the plane, FP, as shown. These are components of the weight, FW1.

The force of friction, FF, is found by using the coefficient of friction:

The mass of Dr. J's box and contents, M1, can be determined from its weight:

The net force can be expressed in two different ways: Knowing the acceleration of the system, we can use Newton's Second Law where M2 represents the total mass of Cy's box and contents.

By finding the vector sum of all the forces we get:

By setting these two expressions for net force equal to each other, M2 can be calculated:

The weight of Cy's box and contents, FW2, can then be determined:

Cy's weight, FWc, can finally be calculated by subtracting the 50 N weight of the box and dividing by 10 (remember, Cy was joined in the box by 9 identical clones):

forces inertia, mass, weight newton’s law types of forces free-body diagram friction

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