Consider the track shown in figure 1. A block of mass 10kg is released from rest

Question

Consider the track shown in figure 1. A block of mass 10kg is released from rest at point A. Section AB of the track is frictionless. Section BD is rough and the coefficient of kinetic friction between the surfaces is k = 0.2. A spring with a spring constant 600 N/m is fixed to the wall at D.

a) find the speed of the block at point C (just before it hits the spring).

b) how far does the block compress the spring?

c) determine the maximum height to which the block rises after it leaves the spring.

Explanation / Answer

.5*m*v^2= m*g*2 or, v= 6.26m/s at B for B to C, friction force acts.... friction force= 10*9.81*.2= 19.62 N decelaration= 19.62/10= 1.96m/s^2 v^2= u^2- 2*a*s or, v^2= 6.26^2-2*1.96*3 or, v=5.24m/s at C .5*m*v^2= .5*k*x^2 or, 10*5.24^2= 600*x^2 or, x=.68 m= 68cm when it leaves the spring, v=5.24m/s again it will go through the B-C region so, V^2(at B)= 5.24^2-2*1.96*3 or, V (at B)= 3.96m/s again energy conservation, .5*m*3.96^2= m*9.81*h or, h=.8m

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