Question

A block having a mass of 0.8 kg is given an initial velocity v = 1.2 m/s to the right and collides

with a spring of negligible mass and force constant k = 50 N/m. Assuming the surface to be
frictionless, calculate the maximum compression of the
spring after the collision.

Answer 1

The maximum compression of the spring after the collision is 0.15 m

Step-by-step explanation:

Given data

Mass of the block (m) = 0.80 kg

Initial velocity (v) = 1.2 m/s

Spring constant (k) = 50 N/m

Find the maximum compression of the spring (x) after compression

Potential energy of the spring = Kinetic energy of the block

Kinetic energy of the block = 0.5 × (mv)²

Kinetic energy of the block = 0.5 × (0.80 × 1.2)²

Kinetic energy of the block =0.5 × 0.9216

Kinetic energy of the block = 0.4608 ---------->(1)

Potential energy of the spring = 0.5 × k × x²

Potential energy of the spring = 0.5 × 50 × x²

Potential energy of the spring = 25 x² ---------> (2)

Equate (1) and (2)

25 x² = 0.4608

x² = 0.018432 m²

x =0.1357 = 0.15 m

Therefore the maximum compression of the spring after collision is 0.15 m