SAT Physics Subject Test

Chapter 3 Newton’s Laws

INCLINED PLANES

An inclined plane is basically a ramp. If an object of mass, m, is on the ramp, then the force of gravity on the object, Fw = mg, has two components: one that’s parallel to the ramp (mg sinθ) and one that’s normal to the ramp (mg cosθ), where θ is the incline angle. The force driving the block down the inclined plane is the component of the block’s weight that’s parallel to the ramp: mg sinθ.

21. A block slides down a frictionless, inclined plane that makes a 30˚ angle with the horizontal. Find the acceleration of this block.

Which Component?

To avoid drawing a free
body diagram for every
inclined plane problem,
remember that mg sinθ is
the component of
gravity down the inclined
plane by thinking “sine”
equals “sliding.”

Here’s How to Crack It

Let m be the mass of the block, so the force that pulls the block down the incline is mg sinθ, and the block’s acceleration down the plane is

22. A block slides down an inclined plane that makes an angle θ with the horizontal. If the coefficient of kinetic friction is µ, find the acceleration of the block.

Here’s How to Crack It

First draw a free-body diagram. Notice that in the diagram shown below, the weight of the block, Fw = mg, has been written in terms of its scalar components: Fw sin θ parallel to the ramp, and Fw cos θ normal to the ramp.

The force of friction, Ff, that acts up the ramp (opposite to the direction in which the block slides) has magnitude Ff = µFN. But the diagram shows that FN = Fw cosθ, so Ff = µ(mg cosθ). Therefore, the net force down the ramp is

Fw sinθ – Ff = mg sinθ – µmg cosθ = mg(sin θ– µcos θ).

Then, setting Fnet equal to ma, we solve for a: