A lump of clay is a projectile at the peak of its parabolic arc when it suddenly explodes into three lumps of equal mass. The initial velocities of those lumps at the moment just after the explosion are:

Lump A: 4.00 m/s traveling due east;Lump B: 3.00 m/s traveling due west;Lump C: 2.00 m/s due north.

Find the velocity of the lump (both magnitude and angle) just before the explosion.

• 2.24 m/s 63.4°• 3.00 m/s 45.0°• 5.00 m/s 30.0°• 2.24 m/s 26.6°• None of the above.

10/19/15 1Oregon State University PH 211, Class #10

A 1000 kg boxcar is collecting 10kg of rain per hour. What will the velocity of the box car be after 3 hours? (Ignore friction/drag)

vi = 22 m/s

10/19/15 2Oregon State University PH 211, Class #10

If +x is to the right, this cart’s change of momentum is

1. –30 kg m/s.2. –20 kg m/s.3. –10 kg m/s.4. 10 kg m/s.5. 30 kg m/s.

10/19/15 3Oregon State University PH 211, Class #10

A person attempts to knock down a large wooden bowling pin by throwing a ball at it. The person has two balls of equal size and mass, one made of rubber, the other of putty. The rubber ball bounces back, while the ball of putty sticks to the pin. Which ball is more likely to topple the bowling pin?

1. the rubber ball

2. the ball of putty

3. makes no difference

4. need more information

10/19/15 4Oregon State University PH 211, Class #10

Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown in the figure, is the cart put in motion?

1. Yes, it moves to the right.

2. Yes, it moves to the left.

3. No, it remains in place.

10/19/15 5Oregon State University PH 211, Class #10

Momentum, by itself, is not that useful (or exciting). It gets more interesting when it’s changing. For example, to hit a baseball a long way (by changing its momentum in a big way), you’d do best to increase both the force of the bat on the ball (how hard you swing), and the time of contact between the bat and ball (follow-through.)

Indeed, Newton defined impulse as the (average) force on an object multiplied by the time during which the force is applied: J = FΔt

10/19/15 6Oregon State University PH 211, Class #10

Impulse-Momentum Theorem

“The impulse applied to an object is the change in momentum of that object.”

J = FavgΔt = mΔv = Δp

 

To catch a water balloon, egg, or (barehanded) a baseball, you need to change its momentum to zero. This is a fixed value, Δp, for a given mass and impact. “Cushioning” your catch extends the interaction time, thus decreasing the force.

10/19/15 7Oregon State University PH 211, Class #10

Or…

Note that the units for impulse will be N s.

These must be the same as kg·m/s!

The time-function version of the theorem lets us do problems when the force is not a constant value—useful if the force can be approximated as a function of time, perhaps the thrust of a solid booster rocket engine.

10/19/15 8Oregon State University PH 211, Class #10

To summarize:

Problems dealing with collisions or explosions of multiple objects (comparing the “before” picture to the “after” picture) use conservation of momentum.

For problems analyzing the processes during the collision (especially for a single object at a time), you’re most likely going to use the Impulse-Momentum relationship:

pFdt

10/19/15 9Oregon State University PH 211, Class #10

Notice the units of the area under the graph.

Impulse J

t

Fdock.truckBeg

inni

ng o

f col

lisio

n an

d

com

pres

sion

of o

bjec

t. End of collision and

restitution of object.

10/19/15 10Oregon State University PH 211, Class #10

A truck with a total mass of 5000 kg traveling at 3.0 km/h hits a loading dock and comes to a stop in 0.6 s. What is the average force exerted by the dock on the truck?