Question

A mass of 1.8 kilograms is placed at height 0.5 meters above the dotted line above on a planar surface inclined at an angle of 30 degrees to the horizontal. The coefficient of kinetic friction between the mass and the inclined portion of the surface is 0.26. The mass is released, slides down the incline and compresses a spring with spring constant 1037.7 N/m. What is the largest compression in meters experienced by this spring?

Answer 1

Hi,

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We know that, Acceleration of the mass sliding down the inclined plane (with friction is given by),

Where,

is acceleration due to gravity (m/s²).

is the angle of inclination.

is The coefficient of kinetic friction ​​​​​​.

Given that,

Acceleration due to gravity,

Angle of inclination,

Coefficient of kinetic friction of surface,

Acceleration of the mass sliding down the inclined plane is given by,

We know that, Work done for sliding down is given by,

Where,

is the force (N).

is distance of sliding (m).

is mass of body (kg).

is acceleration of the block (m/s²).

The sliding distance can be found by simply drawing a free body diagram,

Work done for sliding down is given by,

This work will be stored as energy in the spring (work done to compress the spring):

Given that,

Spring constant of the spring,

Compression of the spring is given by,

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