Question

A block of mass m = 2.90 kg slides along a horizontal table with velocity v 0 = 2.00 m/s . At x = 0 , it hits a spring with spring constant k = 33.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by μ = 0.400 . How far has the spring compressed by the time the block first momentarily comes to rest? Assume the positive direction is to the right.

Answer 1

Gravitational acceleration = g = 9.81 m/s2

Mass of the block = m = 2.9 kg

Initial velocity of the block = V = 2 m/s

Normal force on the block from the table = N

N = mg

Coefficient of kinetic friction between the table and the block = = 0.4

Friction force on the block = f

f = N

f = mg

Force constant of the spring = k = 33 N/m

Distance the spring is compressed when the block momentarily comes to rest = X

By conservation of energy the initial kinetic energy of the block is equal to the potential energy of the spring when the block comes to rest plus the work done against friction.

X = 0.341 m or -1.03 m

Distance cannot be negative.

X = 0.341 m

Distance the spring is compressed by the block when it momentarily comes to rest = 0.341 m