cp.solutions

							                            WebAssign - Collisions 3/18/10 - Solutions




1. A 0.13 kg baseball moving at +26.80 m/s is slowed to a stop by a catcher who exerts a constant
   force of -355 N.
       a. How long does it take this force to stop the ball?




        b. How far does the ball travel before stopping?




2. Two carts with masses of 4.14 kg and 2.32 kg move toward each other on a frictionless track
   with speeds of 4.96 m/s and 3.39 m/s respectively. The carts stick together after colliding head-
   on. Find the final speed.



    Solve for final velocity, as the question asks for speed, use a positive answer.


3. An 76.5 kg fullback moving east with a speed of 5.8 m/s is tackled by a 82.0 kg opponent running
   west at 2.80 m/s, and the collision is perfectly inelastic.
       a. Calculate the velocity of the players just after the tackle.




            Solve for final velocity.

        b. Calculate the decrease in kinetic energy during the collision.




            Solve for change in kinetic energy. This number will be negative, but as the question
            asks for decrease, you use a positive answer.
4. A billiard ball traveling at 3.6 m/s has an elastic head-on collision with a billiard ball of equal
   mass that is initially at rest. The first ball is at rest after the collision. What is the speed of the
   second ball after the collision?

As momentum must be conserved, and both balls have the same mass, if the first ball stops, the
second will acquire all of its momentum. As they have the same mass, the second ball will take on
the velocity of the first: 3.6 m/s. Remember, this only works since it is an elastic collision.



5. A 4.9 g dart is fired into a block of wood with a mass of 23.6 g. The wood block is initially at rest
   on a 1.7 m tall post. After the collision, the wood block and dart land 3.5 m from the base of the
   post. Find the initial speed of the dart.

First, solve the projectile motion problem for the velocity at which the combined block and dart are
traveling off the pedestal. Use the following equation using vertical components:




Solve for time, then solve for horizontal velocity. As initial vertical velocity is zero, the velocity at
which it leaves the pedestal in the horizontal direction will be as follows…




Use that velocity as the final velocity in the inelastic collision. The momentum of the block is not
included as it is at rest.



Solve for initial velocity of the dart.
    6. A 0.15 kg ball of dough is thrown straight up into the air with an initial speed of 6.0 m/s.
           a. Find the momentum of the ball of dough at its maximum height.

            As the vertical component of velocity at the peak height of a projectile’s path is always zero,
            and momentum is mass times velocity, this answer is always zero.

            b. Find the momentum of the ball of dough halfway to its maximum height on the way up.

Use kinetic energy and the knowledge that mechanical energy is conserved so that at half-way, we have
half the starting kinetic energy.




    7. A 774 N student stands in the middle of a frozen pond having a radius of 5.8 m. He is unable to
       get to the other side because of a lack of friction between his shoes and the ice. To overcome
       this difficulty, he throws his 2.3 kg physics textbook horizontally toward the north shore at a
       speed of 5.6 m/s. How long does it take him to reach the south shore?




Solve for the student’s final velocity then….




…using the final velocity and the radius as your displacement. This should be a positive answer (velocity
and displacement should have the same sign either way).