Two people, Aaron and Bethany, are sitting on wheeled carts that can roll withou

Question

Two people, Aaron and Bethany, are sitting on wheeled carts that can roll without friction. Suppose that each person (together with their cart) hns a mass of M 70 kg, and Aaron carres a ball of mass m = 7 kg. (The ball can roll without friction as well.) Note: In this problem a picture will help you keep this straight! 1. Suppose that Aaron rolls the ball to Bethany at UB 4 m/s when it reaches Bethany, she catches it. What will Aaron and Bethany's velocities be after this process? 2. After this happens, do the two of them have the same speed? Is this consistent with the conservation of momentum? 3. Now, suppose that Bethany rolls the ball back to Aaron. She also rolls it at vp2 4 m/s, relative to the motion of her cart. After Aarou catches the ball this time, how fast will he be moving? How fast will Bethany be moving?

Explanation / Answer

given two people A and B, M = 70 kg each and m = 7 kg each

a. Aron rolls the ball to bethany at vb = 4 m/s

after this speed of aron = ua

speed of ball = ub = vb = 4 m/s

in opposite directions

then fromconservation of moemntum

Mua = mub

ua = 0.4 m/s

hence when B catches the ball, from conservation of momentum

speed of B = ub

then

mvb = (M + m)ub

ub = vb*m/(m + M) = 0.363636363636363 m/s

hence velocityies of A and B will not be the same after this process

b. both have differnet speeds

from conservation of momentum

Mua = (M + m)ub

ub = 70*0.4/(77) = 0.36363636363 m/s

hence this is valid form the conservation of meomentum of the total system point of view

c. when B rolls ball back to aron at vb = 4 m/s

when A catches the ball, its speed = u'a

from conservation of moemntum

Mua + m(vb - ub) = (M + m)u'a

u'a = 0.69421487603 m/s

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