<p>Hi,
I'm preparing for AP Physics B and I'm using the PR book.
I have some problems with the free response questions about momentum. I never get my answer to match the one in the book and I don't understand the explanation the book gives. Here are the 2 questions:</p>
<ol>
<li>A steel ball of mass m is fastened to a light cord of length L and released when the cord is horizontal. At the bottom of its path, the ball strikes a hard plastic box of mass M=4m, initially at rest on a frictionless surface. The collision is elastic.</li>
</ol>
<p>a. Find the tension in the cord when the ball's height above its lowest position is 0.5L. Answer in terms of m and g.
b. Find the speed of the block immediately after the collision.
c. To what height h will the ball rebound after the collision?</p>
<ol>
<li>A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block and as a result of the perfectly inelastic impact, the block swings upward. Consider a bullet of mass m with velocity v as it enters the block of mass M. The length of the cords supporting the block each have length L. The max height to which the block swings upward after impact is denoted by y, and the max horizontal displacement is denoted by x.</li>
</ol>
<p>a. In terms of m, M, g, and y, determine the speed of the bullet.
b. What fraction of the bullet's original kinetic energy is lost a s a result of the collision?
c. If y is very small (so that y^2 can be neglected), determine the speed of the bullet in terms of m, M, g, x, and L.</p>
<p>Here are the answers. I just don't know where they came from.</p>
<ol>
<li>
a. 1.5mg
b. 0.4sqrt(2gL)
c. 9L/25</li>
</ol>
<p>2.
a. m+M(sqrt(2gy))/m
b. K(-M)/(m+M)
c. (m+M/m)(x)(sqrt(g/L))</p>
<p>Thanks for all the help. I really appreciate it.</p>