Luke is playing with a gadget that launches a small block with a mass of 20 g us

Question

Luke is playing with a gadget that launches a small block with a mass of 20 g using a spring with a spring constant of 743 N/m. There is no friction or drag acting on the spring or block at any time.

1) Is the kinetic energy of the block when it leaves the spring greater than, less than, or equal to the potential energy stored in the spring when it is fully compressed? Explain your answer.

2) If the spring was compressed 3 cm, what is the speed of the block when it leaves the spring? Show all work

Explanation / Answer

1) the kinetic energy of the block when it leaves the spring = the potential energy stored in the spring when it is fully compressed

here mechanical energy is conserved.

As the compression of the spring decreases potentail decreases but kinetic energy of the block increases.

2) Apply, Energy conservation

final kinetic energy of the block = initial potentail energy stored in the spring.

(1/2)*m*v^2 = (1/2)*k*x^2

v = x*sqrt(k/m)

= 0.03*sqrt(743/0.02)

= 5.78 m/s

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