Question

1. A box of mass 5kg moves to the left at a speed of 6m/s. The box is moving toward an unstretched spring of spring constant 500N/m that is attached to a barrier. If the floor is frictionless, how much does the spring compress in bringing the box to rest? If instead the floor has a coefficient of friction of 0.4, how much does the spring compress in bringing the box to rest?

Answer 1

Part A

The floor is frictionless

Mass of the box = m = 5 kg

Force constant of the spring = k = 500 N/m

Speed of the box = V = 6 m/s

Distance the spring compresses as the box comes to rest = X

By conservation of energy the initial kinetic energy of the box is converted to the potential energy of the spring as it is brough to rest.

X = 0.6 m

Part B

Friction is present between the floor and the box.

Gravitational acceleration = g = 9.81 m/s2

Mass of the box = m = 5 kg

Force constant of the spring = k = 500 N/m

Speed of the box = V = 6 m/s

Distance the box compresses the spring = X

Normal force on the box from the floor = N = mg

Coefficient of friction between the floor and the box = = 0.4

Friction force on the box = f

The initial kinetic energy of the box is equal to the potential energy gained by the spring and the work done against friction as the box comes to rest.

X = 0.562 m or -0.641 m

Distance cannot be negative.

X = 0.562 m

A) Distance the spring compresses to bring the box to rest when the floor is frictionless = 0.6 m

B) Distance the spring compresses to bring the box to rest when friction exists = 0.562 m