A 3 kg object is sliding to the left on a surface with a coefficient of friction of 0.2 at an initial velocity of 15 m/s. Determine the magnitude and direction of the acceleration of this object.

Question

Calculate the acceleration of an object sliding on a flat rough surface (meaning there is friction).

Answer 1

We know that the acceleration will be to the right, since the object is moving left and slowing down, and the surface is flat. Gravitational and normal forces will cancel out, and are vertical anyway, so we just need to find the magnitude of the frictional force.

The frictional force has magnitude μN, where μ=0.2 is your coefficient of friction, and N is the magnitude of the normal force.

Since gravitational and normal forces cancel, the magnitude of N is equal to the magnitude of the gravitational force, which is the mass of your object times the gravitational constant, 3g.

So the friction force is (0.2)(3g), and since this is the only net force on the object, the net acceleration will be the net force divided by the mass (since F=ma), so the magnitude of the acceleration is (0.2)(3g)/3=0.2g≈1.96 m/s².

The initial velocity is irrelevant.