Homework Problems

Linear Momentum

 At this point in your physics life, things seem confusing enough. We have been dealing with three different ways to describe how things move:
1)there was the kinematical description of how objects move;
2) there is the dynamic analysis that comes with using Newton's second law;
3) then there were the prescriptions that apply with the law of conservation of energy.

Now comes a fourth set of considerations made manifest in the law of conservation of linear momentum. There are two general circumstances where this latest rule is applied: 1) two objects are separated and come together in a collision; or, 2) two objects are initially bound together and burst apart. In either case, the conservation law must be applied; there is no way to circumvent this rule by applying an earlier problem-solving protocol. Proceed as follows:

1. Draw a picture.
2. Momentum is a vector whose direction is determined by the direction of its velocity. Assign negative velocities as necessary.3
3. If it given that the event is elastic, you may use the equations on page 6, lines 3 & 4. Otherwise, stick to page 6, lines 1 & 2.
4. If you must prove that a collision is elastic, calculate the KE of each object before and after the collision.

 


 1. Block 1, M1 = 3 kg, slides without friction on a surface at 4 m/s and collides with and sticks to block 2, M2 = 5 kg, initially at rest. a) What is the velocity of the blocks after the collision? b) Is this collision elastic? c) What fraction of the original KE is lost?
solution

  2. A ball, mass M1, is attached to a string of length L; the string is stretched to the 9 o'clock position. See problem WE-1. The ball is released and swings down to 6 o'clock where it collides with a block M2, M2 > M1, initially at rest. The blocks stick together a) To what height do they rise? b) What fraction of the original energy introduced to the system is “lost”?

 3. Same premise as #2 except he collision is perfectly elastic. a) What is the velocity of block 2 after the collision? b) What happens to block 1 after the collision?

 4. A system called a ballistic pendulum consists of a block, MB = 9.95 kg, suspended from a long cord. A bullet, Mb = .05 kg, is fired into the block, embedding itself therein and causing the bullet block combo to rise 25 cm. a) What was the initial speed of the bullet? b) What fraction of the original energy of the bullet is “lost”? Where did it go?

 5. Only in a physics problem would this event happen. This time the 9.95 kg block rests on a horizontal surface where u = .3. The fired bullet (Mb = .05 kg) embeds itself in the block and together they slide on the surface a distance of 6 m before coming to rest. What was the initial speed of the bullet?

 6.A 5 kg block is moving at 3 m/s at the top of a hill 4 m high. Now it slides down the hill. A)How fast is moving at the bottom of the hill? Now the block collides with and sticks to a second block M2 = 1kg. B) How fast are they moving now? C) All of this is happening at the edge of a plateau which drops to a lower level 10 m Below. How far from the base of the cliff do the blocks land??

7. Car A, mass= 1000 kg, travels eastbound at 20 m/s. Car B, mass = 1200 kg, travels northbound at 15 m/s. In the collision that is sure to follow, the vehicles lock together. A) What is their speed and direction after the collision?. B ) What fraction of the original KE is lost?

8. Golfers,desiring to get greater distance off the tee, often select a driver with a massive club head. Assume that the collision between club and ball to be elastic and show that, at most, the speed of the ball will be no more than twice the club speed.

8. Block A, mass = 2 kg, is positioned at the base of a vertical loop whose radius = 1 m Block B, mass = 3 kg, collides with A.. What should be the speed of block B before the collision if A) the block stick together in both make it through the loop; B.) the collision is elastic and only block A makes it through the loop; C.) the collision is elastic and both make it through the loop?

10. You are skating on a pond with a younger sibling. Take your mass to be 60 kg and that of your sibling to be 40 kg. Consider the ice to be friction free. If you pushed off your sibling, sending him away at 4 m/s, what speed you expect to have as a result of this action?

11. At the railroad yard, we find a gondola car that is watertight and moving by itself at 1 m/s The mass of the car is 10, 000 kg. It's a rainy day today and while the car is moving it picks up a 1000 kg of rainwater. How fast is this car moving now that it has acquired this new load?

12. One of my toys is a five-ball collision apparatus that is intended to simulate elastic collision.. If two balls are displaced and strike the others, two balls emerge from the other side. Show that it is not possible to send in a all at a speed V and have one ball emerge at the speed of two times V.

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