Question

A car of mass 1000kg moving with a speed of 18km/h on a smooth road and colliding with a horizontally mounted spring of spring constant 6.25*1000N/m. What is the maximum compression of the spring?​

Answer 1

Answer:

The maximum compression for the spring is 2 meters.

Explanation:

Here, we will apply the law of conservation of Kinetic energy.

Now, let x be the maximum compression of the spring.

The kinetic energy of the spring is given by:

KE = 1/2kx² where k is the spring constant.

The kinetic energy of the Car is given by:

KE = 1/2mv², where m is the mass of the car and v is the speed at which it is moving.

We convert the speed to the SI unit which is m/s

We have: 18 × 5/18 = 5 m/s

Substituting we have:

1/2 × 1000 × 5² = 12500 Joules

Now, by law of conservation of kinetic energy, initial kinetic energy equals to final kinetic energy.

Equating the two we have:

12500 = 0.5x² × 6.25 × 1000

x² = 12500/3125

x² = 4

x = 2

The maximum compression for the spring is 2 meters.

Answer 2

Answer:

Maximum compression of the spring is 2m