H2 Physics 3 - Motion and Forces: Object on an Inclined Plane

Step 1 - Set up the problem

A 5 kg block sits on a smooth inclined plane at 30 degrees.

Step 1 - Set up the problem

It is released from rest. Find the acceleration down the plane and the normal reaction.

Step 1 - Set up the problem

Take g = 9.81 m/s squared.

Step 2 - Resolve weight along and perpendicular to the plane

Weight = mg = 5 times 9.81 = 49.05 N.

Step 2 - Resolve weight along and perpendicular to the plane

Resolve into components: mg sin theta along the plane, mg cos theta perpendicular.

Step 2 - Resolve weight along and perpendicular to the plane

Down the slope: 49.05 times sin 30 = 24.5 N.

Step 3 - Apply Newton's second law along the plane

Along the plane, the only force is mg sin theta (no friction).

Step 3 - Apply Newton's second law along the plane

By F = ma: ma = mg sin theta.

Step 3 - Apply Newton's second law along the plane

Mass cancels: a = g sin theta = 9.81 times sin 30.

Step 3 - Apply Newton's second law along the plane

a = 4.91 m/s squared down the slope.

Step 4 - Find the normal reaction

Perpendicular to the plane, there is no acceleration.

Step 4 - Find the normal reaction

So N = mg cos theta.

Step 4 - Find the normal reaction

N = 49.05 times cos 30 = 42.5 N.

Step 5 - State the final answers

Acceleration down the slope: 4.91 m/s squared.

Step 5 - State the final answers

Normal reaction: 42.5 N perpendicular to the surface.

Step 5 - State the final answers

Key insight: acceleration is independent of mass - just like free fall, but along the slope.