Question

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

Options

• 8.5 cm

• 5.5 cm

• 2.5 cm

• 11.0 cm

Answer 1

A 2 kg block slides on a horizontal floor with a speed of 4m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compresses by 5.5 cm.

Explanation:

Suppose the spring gets compressed by x before stopping.

kinetic energy of the block = P.E. stored in the spring + work done against friction.

⇒ `1/2xx2xx(4)^2= 1/2xx10,000xxx^2+15xxx`

⇒ 10,000x² + 30x - 32 = 0

⇒ 5000x² + 15 x - 16 = 0

∴ x = `(-15±sqrt((15)^2-4xx(5000)(-16)))/(2xx5000)`

= 0.055 m 

= 5.5 cm.