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Unformatted text preview: Solution for Long-answer Homework 10 Reference Frames problems Solution to Long-answer Homework Problem 10.1(Explosive Collision) Problem: Cart 1 ( m 1 = 0 . 3kg ) has two vials of volatile chemicals attached to the front of it. The cart is travelling at a velocity of +20 m s with respect to the earth as it collides with another cart ( m 2 = 0 . 5kg ), moving at +10 m s with respect to the earth. When the carts collide, the vials break and the chemicals mix, resulting in an explosion that causes the two carts to rocket away from each other in opposite directions. Immediately after the collision, the kinetic energy of the system is increased by 30% . (a)What is the kinetic energy of the system just before the collision? (b)What is the momentum of the system in the earths frame of reference? (c)What is the magnitude of the relative velocity of the system immediately after the collision? (d)What are the velocities of the two carts, immediately after the collision? Solution to Part (a) Apply definition: K sys = K 1 + K 2 = 1 2 m 1 v 2 1 ,i + 1 2 m 2 v 2 2 ,i = 85J Grading Key: Part (a) 3 Points 2 point(s) : Correctly calculated kinetic energies 1 point(s) : add them Solution to Part (b) Use our friend, conservation of linear momentum: p sys = m 1 v 1 ,i + m 2 v 2 ,i Now we can plug in and solve. p sys = (0 . 3kg) parenleftBig 20 m s parenrightBig + (0 . 5kg) parenleftBig 10 m s parenrightBig p sys = 11 . 0kg m s Grading Key: Part (b) 3 Points 1 point(s) : use conservation of linear momentum 2 point(s) : one point for momentum of each cart Solution to Part (c) Using the relationship v rel = v 2- v 1 (could be 1-2, doesnt matter, as long as we are consistent) v rel,i = 10 m s- 20 m s =- 10 m s 1 The change in kinetic energy is . 3 K sys,i = 25 . 5J Reduced mass, , is given by = m 1 m 2 m 1 + m 2 = (0 . 5kg)(0 . 3kg) (0 . 5kg + 0 . 3kg) = 0 . 1875kg Use the change in kinetic energy and the relative initial velocity to find the final velocity. K sys = 1 2 ( v 2 rel,f- v 2 rel,i ) 25 . 5J = 1 2 (0 . 1875kg) parenleftbigg v 2 rel,f- parenleftBig- 10 m s parenrightBig 2 parenrightbigg This gives v rel,f = | 19 . 3 m s | . Grading Key: Part (c) 5 Points 1 point(s) : change in kinetic energy, . 3 K sys,i ....
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