2. In the figure below, a block of mass m 5 kg is compressed 50 cm against a spr

Question

2. In the figure below, a block of mass m 5 kg is compressed 50 cm against a spring with spring constant k-6480 N/m. The block is let go and slides across a frictionless surface until it encounters point A where the track curves upward at an angle of 35° At a distance h above the horizontal portion of the track, the block encounters a surface with a coefficient of friction of u 0.24. The block slides a distance L 1.57 m across this surface until it encounters point B. Determine the block's velocity at point B. 50 cm h: 2.om

Explanation / Answer

Net workdone on the block = W_spring + W_gravity + W_friction + W_normal

= (1/2)*k*x^2 - (m*g*h + m*g*L*sin(35)) - fk*L + 0

= (1/2)*k*x^2 - (m*g*h + m*g*L*sin(35)) - mue_k*m*g*cos(35)*L + 0

= (1/2)*6480*0.5^2 - (5*9.8*2 + 5*9.8*1.57*sin(35)) - 0.24*5*9.8*cos(35)*1.57 + 0

= 653 J

using work-energy theorem,

Wnet = (1/2)*m*(vf^2 - vi^2)

Wnet = (1/2)*m*vf^2 (since vi = 0 )

vf = sqrt(2*Wnet/m)

= sqrt(2*653/5)

= 16.2 m/s

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