The 3 kg object in Figure 7-18 is released from rest at a height of 5 m on a cur

Question

The 3 kg object in Figure 7-18 is released from rest at a height of 5 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant k = 450 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest.

1. Find x.

The 3 kg object in Figure 7-18 is released from rest at a height of 5 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant k = 450 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. Find x.

Explanation / Answer

total mechanical energy the block has before sliding = mgh = 3*9.8*5 =147J

total mechanical energy the block has when it reaches ground = 1/2*mv^2 = mgh = 147J

=> v=9.899m/s

when block becomes to rest its kinetic enegy = 0 the spring compresses a distance x

there fore 1/2kx^2= 1/2*mv^2= 147 => x= 0.8083 m

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