A 400 g bock is dropped onto a relaxed vertical spring that has a spring constan

Question

A 400 g bock is dropped onto a relaxed vertical spring that has a spring constant of 3 N/cm. The block becomes attached to the spring and compresses the spring 10 cm before turning around.

(a) What work is done on the block by the gravitational force on it while the spring is being compressed?

(b) What work is done on the block by the spring force on it while the spring is being compressed?

(c) What is the speed of the block just before it hits the spring?

(d) If the speed at impact is doubled, what is the maximum compression of the spring?

Explanation / Answer

a) work done by the gravitational force is m*g*h = 0.4*9.8*0.1 = 0.392 J

b) Work done by the spring Force is W = 0.5*k*x^2 = 0.5*300*0.1^2 = 1.5 J

c) Work done by the Net force = chance in kinetic energy

0.392 + 1.5 = 0.5*m*(V^2)

0.392+1.5 = 0.5*0.4*V^2

V = 3.075 m/sec

d) if the speed is doubled,then

m*g*x + (0.5*k*x^2) = 0.5*m*v^2

(0.4*9.8*x) + (0.5*300*x^2) = 0.5*0.4*(2*3.075^2)

x = 0.146 m = 14.6 cm

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