How Does the Angle of an Incline Affect Acceleration?

[aege125]

Is the acceleration of an object going down an inclined surface directly proportional to the angle of the inclined surface? (is there a linear relationship between the angle and acceleration?)

What are the factors that affect the change of the acceleration? (is it mass and friction?)

Is there a formula for this?

 

[DavidWhitbeck]

What you are asking is a standard example in most introductory physics texts. You should look up the derivation, it is also a great exercise in using Newton's 2nd Law in vector components form.

The result is $$a = g\sin\theta$$

It is (a) independent of mass, (b) constant in time, and (c) is derived assuming that only weight and normal force act on the body.

If a friction force, with a kinetic coefficient of friction $$\mu$$ opposes the motion then the expression becomes

$$a = g(\sin\theta - \mu\cos\theta)$$.