Ch 09 HWA Game of Frictionless Catch A Game of Frictionless Catch Pa Chuck and J

Question

Ch 09 HWA Game of Frictionless Catch A Game of Frictionless Catch Pa Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart, Mcart, is identical to the combined mass of Jackie and her cart Initially, Chuck and Jackie and their carts are at rest. Chuck then picks up a ball of mass mball and throws it to Jackie, who catches it. Assume that the ball travels in a straight line parallel to the ground (ignore the effect of gravity). After Chuck throws the ball, his speed relative to the ground is ve. The speed of the thrown ball relative to the ground is vb Jackie catches the ball when it reaches her, and she and her cart begin to move. Jackie's speed relative to the ground after she catches the ball is vj When answering the questions in this problem, keep the following in mind: 1. The original mass mcart of Chuck and his cart does Par not include the mass of the ball. 2. The speed of an object is the magnitude of its velocity. An object's speed will always be a nonnegative quantity Part

Explanation / Answer

(d) Momentum of Jackie, cart and the ball before Jackie cathes the ball

pi = 0 + 0 + mball vb

pi = mball vb

Momentum of Jackie, cart and the ball after Jackie cathes the ball

pf = 0 + mcart vj + mball vj

pf = (mcart + mball) vj

By conservation of momentum pi = pf

mball vb = (mcart + mball) vj

vj = mball vb / (mcart + mball)

(e) initial momentum of Chuck, cart and the ball pi = 0, as they all are at rest

Final momentum of Chuck, cart and the ball pf = 0 + mcart (-vc) + mball vb

pf = -mcart vc + mball vb

from part (a) we have vc = u - vb

pf = -mcart (u - vb) + mball vb

pf = -mcart u + (mcart + mball ) vb

Now, by conservtion of momentum pi = pf

0 = -mcart u + (mcart + mball ) vb

vb = (mcart u) / (mcart + mball )

And from part (d) we have

vj = mball vb / (mcart + mball)

Elliminating vb from above 2 equations

vj = { mball / (mcart + mball) } * { (mcart u) / (mcart + mball ) }

vj = u mball mcart / (mcart + mball)2

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---