Question

A 2 kg block slides on a horizontal floor with a speed of 4m/s. It strikes a uncompressed spring, and compressed it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000N/m. The spring compressed by

Answer 1

Given,

Mass, m = 2 kg

Initial velocity, u = 4 m s^(-1)

Here the spring is compressed till the block is being motionless, or, till the velocity of the block becomes zero. Then,

Final velocity, v = 0 m s^(-1)

Frictional force, f = 15 N

Spring constant, k = 10,000 N m^(-1)

We have to find the compression of the spring, x.

By work - energy theorem, we have,

Net work done = Change in kinetic energy, i.e.,

15x + (kx² / 2) = m(v² - u²) / 2

15x + (10000x² / 2) = 2(0² - 4²) / 2

15x + 5000x² = 16

(we consider only the magnitude)

5000x² + 15x - 16 = 0

Then,

x = (- 15 + √(4 · 5000 · -16)) / (2 · 5000)

x = 0.0551 m

x = 5.51 cm