1 A block of mass 0.240 kg is placed on top of a light, vertical spring of force

Question

1

A block of mass 0.240 kg is placed on top of a light, vertical spring of force constant 4 950 N/m and pushed downward so that the spring is compressed by 0.108 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise? (Round your answer to two decimal places.)
1 m

2

Dave Johnson, the bronze medalist at the 1992 Olympic decathlon in Barcelona, leaves the ground at the high jump with vertical velocity 5.50 m/s. How far does his center of mass move up as he makes the jump?
1 m

Explanation / Answer

1) mg = kx
(0.240 kg)(9.81 m/s^2) = (4950 N/m)(x)
x = 4.7564e-4 m

OK, this is pretty insignificant compared to the 0.108 m additional compression... to arrive at an answer needing 2 decimal places, so there's little need to account for this. So...

If this means that the block is placed on the spring, the spring compresses slightly due to the weight of the block, then the block is pushed downward to compress the spring another 0.108 m, this would be the calculation:

(initial potential energy of compressed spring) = (final gravitational potential energy of block)
(1/2)kd^2 = mgy
(1/2)(4950 N/m)(0.108 m)^2 = (0.240 kg)(9.81 m/s^2)(y)
y = 12.26 m

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