Consider a block sliding down a frictionless inclined plane with acceleration a . If we double the mass of the block,what is its acceleration?

Question

$\begin{array}{1 1}\large\frac{a}{4}\\\large\frac{a}{2}\\a\\2a\end{array} $

Answer 1

Toolbox:

• All problems in laws-of-motion that concern a frictionless inclined plane can be represented by the diagram below, where N = normal force that is perpendicular to the plane, m = mass of object, g = acceleration due to gravity, $\theta$ (theta) = angle of elevation of the plane, measured from the horizontal
• Component of gravity pushing the block down the incline plane = $mg \sin \theta$
• Component of gravity pushing the block against the incline plane = $mg \cos \theta$

Answer: a.

http://clay6.com/mpaimg/inclined1.png

The acceleration of any particle due to the force of gravity alone doesn't depend on the mass so the answer is a.Whether or not the mass is on an inclined plane doesn't matter in the least bit. we can prove this by calculating the acceleration mathematically :

$F = ma = mg\sin \theta$

$a =g\sin \theta$

As you can see,the acceleration depends only on the angle of the incline and not on the mass of the block.