A block of mass 1kg is sitting on top of a compressed spring of spring constant

Question

A block of mass 1kg is sitting on top of a compressed spring of spring constant k = 300 N m and equilibrium length 20cm. Initially the spring is compressed 10cm, and the block is held in place by someone pushing down on it with his hand. At t = 0, the hand is removed (this involves no work), the spring expands and the block flies upwards.

(a)[6 pts] Draw a free-body diagram for the block while the hand is still pressing down. Try to get the forces approximately to scale. The following question should help.

(b)[3 pts] What must be the force (magnitude and direction) exerted by the hand on the block?

(c)[3 pts] How much elastic potential energy was stored in the spring initially?

(d)[3 pts] Taking the system formed by the block and the earth, how much total work is done on it by the spring, as it expands to its equilibrium length? (You do not need to do a new calculation here, just think of conservation of energy.)

(e)[3 pts] How high does the block rise above its initial position?

(f)[3 pts] Treating the block alone as the system, how much net work is done on it by the two external forces (the spring and gravity) from the time just before it starts moving to the time it reaches its maximum height? (Again, no calculation is necessary if you can justify your answer.)

Explanation / Answer

b)

force pressing the spring = k * x

force pressing the spring = 300 * (0.20 - 0.10)

force pressing the spring = 30 N

the force pressing the spring is 30 N in the left direction

c)

Initial elastic potential energy stored = 0.5 * k * x^2

Initial elastic potential energy stored = 0.5 * 300 * (0.20 - 0.10)^2

Initial elastic potential energy stored = 1.5 J

the Initial elastic potential energy stored is 1.5 J

d)

Total work done by the spring = change in elastic potential energy of spring

Total work done by the spring = 1.5 - 0

Total work done by the spring = 1.5 J

e)

let the height is h

work done by the spring = m * g * h

1.5 = 1 * 9.8 * h

h = 0.153 m

the block will rise to 0.153 m

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