PHYS 2010 Written HW 7 Name: The figure shows a horizontal frictionless surface, two immovable walls, two springs, and two masses. You are going to perform an experiment in which you compress each spring as shown and then release the masses from rest. When the springs reach their equilibrium position, the masses lose contact with the springs, and the masses head toward each other on a collision course. What will happen next? frictionless surface 1) What principle of physics will you use to find the speed of each mass just after it loses contact with its spring? Just write the name the equation/theorem here. 2) Derive an expression for the speed (call it $v_{m}$ ) of the block of mass $m$ just after it loses contact with its spring. Your answer should be a formula in terms of the variables given in the figure. 3) Now derive an expression for the speed of the block of mass $4 m$. Express your answer in terms of $v_{m}$ [For example, $v_{4 m}=\frac{13}{27} v_{m}$. That's not right, but you get the idea...]

PHYS 2010 Written HW 7 Name: 4) Indicate your positive direction and the directions of the momenta. 5) The block with the largest magnitude momentum is block of mass... $m \quad 4 m$ (circle one) Show your work here: 6) The total momentum of the system is a vector pointing to the... right left (circle one) 7) Write an expression for the magnitude of the total momentum of the system in terms of just $m$ and $v_{m}$. 8) The two masses collide and stick to each other. What principle of physics will you use to find the velocity of the (stuck together) masses? Just write the name of the equation/theorem here. 9) Derive an expression for the velocity of the (stuck together) masses after the collision in terms of just $v_{m}$. [For example, $v_{5 m}=\frac{13}{27} v_{m}$. That's not right, but you get the idea..]

PHYS 2010 Written HW 7 Name: 10) The (stuck together) masses after the collision are moving to the... right left (circle one) 11) The (stuck together) masses will collide with, and compress, one of the springs. Although the spring will then re-launch the masses back toward the center, let's just talk about the compression phase for now. What principle of physics will you use to find the maximum compression of the spring? Just write the name of the equation/theorem here. 12) Derive an expression for the maximum compression of the spring. Lots of variable cancellations should occur and your final answer should depend only on dl