An air-track cart of mass 0.10 kg is moving with a speed 1.4 m/s to the right wh

Question

An air-track cart of mass 0.10 kg is moving with a speed 1.4 m/s to the right when it collides with a cart of mass 0.21 kg that is at rest. Each cart has a wad of putty on its bumper, and hence they stick together as a result of their collision. Suppose the average contact force between the carts is 1.0 N during the collision. What is the magnitude of the acceleration of cart 1? Express your answer using two significant figures. What is the direction of the acceleration of cart 1? What is the magnitude of the acceleration of cart 2? What is the direction of the acceleration of cart 2? How long does it take for both carts to have the same speed? (Once the carts have the same speed the collision is over and the contact force vanishes.) What is the final speed of the carts, vf?

Explanation / Answer

m1 = 0.1 kg

u1 = + 1.4 m/s

m2 = 0.21 kg

u2 = 0

P1i = m1*u1 = 0.014

P2i = m2*u2 = 0

after collision

force acting on m1, F1 = -0.1 N

a1 = -1/0.1 = -10 m/s^2     <<-------answer

direection left <<-------answer

force on m2 = F2 = 0.1 N

a2 = F2/m2 = 0.1/0.21 = 0.48 m/s^2 <<-------answer

direction right <<-------answer

from momentum conservation

Pi = Pf

m1*u1 + m2*u2 = (m1+m2)*V

(0.1*1.4)+0 = (0.1+0.21)*V

V = 0.45 m/s

F = m1*(v1-u1)/t

1 = 0.1*(0.45-1.4)/t

t = 0.095 s<------------answer

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