A 5 kg block is placed at the top of a 4-meter-long incline ...

Question

A 5 kg block is placed at the top of a 4-meter-long incline with an angle of 30°. The block starts from rest, and the coefficient of kinetic friction between the block and the incline is 0.2. What is the block's speed when it reaches the bottom of the incline? (Take g = 10 m/s², sin30°=0.5, cos30°=0.87)

To solve this problem, we will use the work-energy principle. The work done on the block is the sum of the work done by the gravitational force and the work done by the frictional force.

Determine the forces involved

1. Gravitational force component along the incline:

Where:

2. Frictional force:

The normal force is given by:

The frictional force is:

Calculate the net work done on the block

1. The total work done on the block is the work done by gravity minus the work done by friction. The displacement along the incline is

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