9.4 Types of Collisions

There is a possible mathematical second to the system of equations solved in this example (because the energy equation is quadratic): $v_{\text{1},\text{f}} = 0 , v_{\text{2},\text{f}} = −2.5 \text{m}/\text{s}$. This solution is unacceptable on physical grounds; what’s wrong with it?

Suppose there had been no friction (the collision happened on ice); that would make $\mu_{\text{k}}$ zero, and thus $v_{\text{c},\text{f}} = \sqrt{2 \mu_{\text{k}} g d} = 0$, which is obviously wrong. What is the mistake in this conclusion?

Two objects of equal mass are moving with equal and opposite velocities when they collide. Can all the kinetic energy be lost in the collision?

A 5.50-kg bowling ball moving at 9.00 m/s collides with a 0.850-kg bowling pin, which is scattered at an angle of 15.8° to the initial direction of the bowling ball and with a speed of 15.0 m/s.

1. Calculate the final velocity (magnitude and direction) of the bowling ball.
2. Is the collision elastic?

A 90.0-kg ice hockey player hits a 0.150-kg puck, giving the puck a velocity of 45.0 m/s. If both are initially at rest and if the ice is frictionless, how far does the player recoil in the time it takes the puck to reach the goal 15.0 m away?

In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assuming that the mass of the drivers is much, much less than that of the bumper cars, what are their final speeds?

An alpha particle (⁴He) undergoes an elastic collision with a stationary uranium nucleus (²³⁵U). What percent of the kinetic energy of the alpha particle is transferred to the uranium nucleus? Assume the collision is one-dimensional.

A 35-kg child rides a relatively massless sled down a hill and then coasts along the flat section at the bottom, where a second 35-kg child jumps on the sled as it passes by her. If the speed of the sled is 3.5 m/s before the second child jumps on, what is its speed after she jumps on?