A horizontal spring with a spring constant of 10N/m is compressed to launch a 5

Question

A horizontal spring with a spring constant of 10N/m is compressed to launch a 5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient is the kinetic friction between the box and the rough surface is 0.2. The box slides 1 m across this surface before it stops. How much was the horizontal spring compressed? A horizontal spring with a spring constant of 10N/m is compressed to launch a 5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient is the kinetic friction between the box and the rough surface is 0.2. The box slides 1 m across this surface before it stops. How much was the horizontal spring compressed?

Explanation / Answer

potential energy in the spring = 1 / 2 k x2

this is transformed as kinetic energy of the mass = 1/2 m v2.

this energy is lost due to friction = F d where F is the frictional force and

d is the distance moved

F = ma where a is the acceleration

1 / 2 k x2 = 1 / 2 m v2

= m a d

k x2 = m v2 =2 m a d

v2 = k x2 / m = 2 a d

d = k x2 / (2 a m)

magnitude of a = g

d = k x2 / (2 g m)

x2 = (2 d g m) / k

x = sqrt(2 d g m) / k

= sqrt(2 x 1 x 0.2 x 9.8 x 5) / 10

= 1.4 m

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