As shown above, a 0.20-kg mass is sliding on a horizontal, frictionless air trac

Question

As shown above, a 0.20-kg mass is sliding on a horizontal, frictionless air track with a speed of 3.0 m/s when it instantaneously hits and sticks to a 1.3-kg mass initially at rest on the track. The 1.3-kg mass is connected to one end of an 8.0-cm long, massless spring, which has a spring constant of 100 N/m. The other end of the spring is fixed. (a) Determine the momentum for the 0.20-kg mass immediately before the impact. (b) Determine velocity of the combined masses immediately after the impact. (c) After the collision, the combined mass compresses the spring and comes momentarily to a rest. Determine the minimum value of the distance between the combined mass and the wall.

Explanation / Answer

According to the given problem,

a) Immedialty beforeimpact is,

Pi = m1v1 = 0.2 *3 = 0.6 kg-m/s

b)Using the conservation linear momentum principal,

P1 = P2

(m1+m2) v = 0.6

v = 0.6/1.5 = 0.4 m/s

c) Using the conservation of Energy principal,

K.E = S.P.E

1/2mv2 = 1/2 kx2

x2 = mv2/k = 1.5*0.42/100 = 2.4*10-3

x = 0.0489 m

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