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Chapter 9: Problem 92
The component of the ball's velocity whose magnitude is most affected by the collisions is a. horizontal. b. vertical. c. Both are affected equally.
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A block of mass \(m_{1}\) undergoes a one-dimensional elastic collision with an initially stationary block of mass \(m_{2} .\) Find an expression for the fraction of the initial kinetic energy transferred to the second block, and plot your result for mass ratios \(m_{1} / m_{2}\) from 0 to 20.
A proton (mass 1 u) moving at 6.90 Mm/s collides elastically head-on with a second particle moving in the opposite direction at \(2.80 \mathrm{Mm} / \mathrm{s}\). After the collision, the proton is moving opposite its initial direction at \(8.62 \mathrm{Mm} / \mathrm{s}\). Find the mass and final velocity of the second particle.
An 11,000 -kg freight car rests against a spring bumper at the end of a railroad track. The spring has constant \(k=0.32 \mathrm{MN} / \mathrm{m}\). The car is hit by a second car of \(9400-\mathrm{kg}\) mass moving at \(8.5 \mathrm{m} / \mathrm{s}\), and the two couple together. Find (a) the maximum compression of the spring and (b) the speed of the two cars when they rebound together from the spring.
Consider a system of three equal-mass particles moving in a plane; their positions are given by \(a_{i} \hat{\imath}+b_{i} \hat{\jmath},\) where \(a_{i}\) and \(b_{i}\) are functions of time with the units of position. Particle 1 has \(a_{1}=3 t^{2}+5\) and \(b_{1}=0 ;\) particle 2 has \(a_{2}=7 t+2\) and \(b_{2}=2 ;\) particle 3 has \(a_{3}=3 t\) and \(b_{3}=2 t+6 .\) Find the center-of-mass position, velocity, and acceleration of the system as functions of time.
Find the center of mass of a uniform slice of pizza with radius \(R\) and angular width \(\theta\).
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