Your friend says that momentum conservation means that the total momentum of a s

Question

Your friend says that momentum conservation means that the total momentum of a system (the sum of the momenta of all the objects in the system) is constant. Do you agree with your friend? If not, what would be a more accurate statement? (b) You can use conservation in order to measure mass. Suppose that you have two carts One has a known mass while the other has an unknown mass. suppose that the carts can be made to roll frictionlessly and that y stick to each other when they collide, how can you determine the unknown mass? You can assume that you have tools for measuring velocities. (c) Rebecca and Josh are standing on nearly frictionless ice, throwing a ball back- and forth. Both of them are about 60 kg and the ball is about 1 kg. Each person can throw the ball so that it leaves their hands travelling at a speed of 20 m/s relative to the thrower. The two start playing their game while initially at rest (c1) Rebecca throws first. How fast does she move after she throws the ball? How fast does Josh move after he catches the ball the first time? (c2) Josh throws the ball back to Rebecca. How do Rebecca and Josh move after Rebecca catches the ball?

Explanation / Answer

a) Momentum is said to be conserved only when the net external force acting on the system is ZERO.

It can be conserved only in that dimension ( say, x-axis) where net external force is zero.

b) Let m= unknown mass, M= known mass, v= velocity of m before collision, V= velocity of M before collision, w= Their combined velocity, after collision.

So, as friction is zero, we can definitely apply the conservation of linear momentum about the axis in which the carts are moving:

mv+MV=(m+M)w

which gives us m (unknown mass)= M(w-V)/(v-w)

c) c1) applyng the conservation of linear momentum for Rebecca,

0= (60 x v) + (1 x 20) Initial speed of ball and Rebecca are zero.

So, v= -20/60 = -1/3= -0.33 m/s (Negative sign shows that she moves backwards, after releasing the ball from her hands)

For Josh,

0= (60 x v) + (1 x 20)

v= -0.33 m/s

c2) Josh should move backwards, (by action-reaction) since he's throwing the ball.

After catching the ball, Rebecca must also move backwards in order to bring the ball's momnetum to zero, by holding it in her hands.

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