Jason, Kim, and twins Ike and Mike are goofing around on a loading dock that is

Question

Jason, Kim, and twins Ike and Mike are goofing around on a loading dock that is 2.5 m above street level. Some old, roll-around desk chairs are left there. Each chair has a mass of 20 kg, and the guys discover that they roll extremely well. Mike (70 kg) gets in one chair, and the other guys push him with a net force of 200 N for some distance before letting him go. They are trying to see if their push will send him up a narrow ramp near the back of the dock (it goes to a second floor level). Unfortunately, they miss, and as Mike and the chair are about to head off the end of the loading dock at 4 m/s, Mike leaps horizontally off the chair, back toward the dock. Jason (plus the chair) weighs twice as much as Mike plus the chair. If the guys had gotten Jason going the same speed as Mike, (A) Jason could have gone 4 times as high up the ramp. (B) Jason could have gone twice as high up the ramp Jason could have gone just as high up the ramp Jason could have gone as high up the ramp. (E) Jason could have gone 1/4 as high up the ramp. If Mike had not leapt off the chair (A) it would have been in the air longer (B) it would have been in the air for less time (C) it would have been in the air for the same time. If Mike's chair had bumped into one of the other chairs, which was also free to roll about, and that chair rolled away after being hit without being slowed by friction, this collision would have most likely (A) conserved momentum, but not mechanical energy (B) conserved mechanical energy, but not momentum (C) conserved both mechanical energy and momentum (D) conserved neither mechanical energy nor momentum. If Mike's twin brother Ike had been in an identical chair rolling toward Mike, so that they stop dead after the collision, then this collision would have (A) conserved momentum, but not mechanical energy (B) conserved mechanical energy, but not momentum (C) conserved both mechanical energy and momentum (D) conserved neither mechanical energy nor momentum.

Explanation / Answer

(14) Let mj = mass of Jason

            mm = mass of Mike

            mc = mass of chair

       Lets first consider motion of Mike in the chair

       m = mm + mc

       Acceleration am = F/m

       using equation vm2 - um2 = 2amdm

    Set um=0, this gives dm = vm2m/2F ------------(1)

Now consider motion of Jason in the chair

    m = mj + mc = 2 (mm + mc) = 2m

   Acceleration a = F/2m

using equation vj2 - uj2 = 2ajdj

Setting uj=0, this gives dj = vj2m/F = vm2m/F (given vj = vm) ----------(2)

Comparing equations (1) and (2) dj = dm/2

(15) Mike and the chair are part of the same system and moving in the same frame of reference. For the vertical motion y = ut + (0.5) at2 , the time is independent of the mass, so even if Mike had not leapt off the chair, himself and the chair would have remained in the air for the same time.

(16) Since there is no friction, energy is conserved. Also in the absence of external force, momentum is conserved. Hence both mechanical energy and momentum are conserved.

(17) Since they collide and come to rest, energy (particularly kinetic energy) is dissipated in the collision. But since there is no external force acting on them, their momentum is conserved.

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