What is the acceleration of the object?

Question

An object with a mass m slides down a rough 37 degree inclined plane where the coefficient of kinetic friction is 0.20. What is the acceleration of the object?

Answer 1

Make free body diagram showing the forces on the object. The forces are

1. Weight mg downward

2. Normal force N perpendicular to plane

3. Friction f = 0.2N up the incline

There is no acceleration perpendicular to plane. Therefore, total force perpendicular to plane = 0

Or, N - mg cos 37 deg = 0

Or, N = mg cos 37 deg = 0.8 mg

Therefore, f = 0.2N = 0.16 mg

Total force along the plane = mg sin 37 deg - f

= 0.6 mg - 0.16 mg = 0.44 mg

Acceleration = force/mass = 0.44 mg/m = 0.44 g = 0.44 * 9.8 m/s^2

= 4.31 m/s^2

Ans: 4.31 m/s^2

Answer 2

First of all  make  free body diagram showing the forces on the object. The forces are

1. Weight mg downward

2. Normal force N perpendicular to plane

3. Friction f = 0.2N up the incline

There is no acceleration perpendicular to plane. Therefore, total force perpendicular to plane = 0

Or, N - mg cos 37 deg = 0

Or, N = mg cos 37 deg = 0.8 mg

Therefore, f = 0.2N = 0.16 mg

Total force along the plane = mg sin 37 deg - f

= 0.6 mg - 0.16 mg = 0.44 mg

Acceleration = force/mass = 0.44 mg/m = 0.44 g = 0.44 * 9.8 m/s^2

= 4.31 m/s^2

Ans: 4.31 m/s^2