A block of mass m slides down a 30 o incline from a height h (starting from rest

Question

A block of mass m slides down a 30o incline from a height h (starting from rest). At the bottom, it strikes a mass M = 3m which is at rest on a horizontal surface (Fig. 5). Assume a smooth transition at the bottom of the incline. If the collision is elastic, and friction can be ignored determine:

(a) the speed of the mass m just before the collision

(b) the speeds of the two blocks after the collision

(c) how far back up the incline the smaller mass m will go,

A block of mass m slides down a 30o incline from a height h (starting from rest). At the bottom, it strikes a mass M = 3m which is at rest on a horizontal surface (Fig. 5). Assume a smooth transition at the bottom of the incline. If the collision is elastic, and friction can be ignored determine: the speed of the mass m just before the collision the speeds of the two blocks after the collision how far back up the incline the smaller mass m will go,

Explanation / Answer

1. height h=30 sin(30) = 30 * 1/2 =15 m

velocity u = sqrt(2*g*h) = sqrt( 2*9.8*15) = 17.14 m/s

2. Using v1 = (m1-m2)/(m1+m2) u1 + 2m2u2/(m1+m2)

u1=17.14 and u2=0

v1 = (-2m/4m)*17.14 = -8.5 m/s

v2 = (m2-m1)/(m1+m2) u2 + 2m1u1/(m1+m2)

v2 = (2m/4m)*17.14

= 8.5 m/s

3.

accelaration a = -g sin 30 = -4.9 m/s^2

s= (v^2 - u^2)/2a

= -73.5/(-9.8)

= 7.5 mtr

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