A Race on Slopes

Classical Mechanics Level 2

Three identical blocks are released from rest simultaneously, from fixed inclined planes having different slopes.

If all surfaces are smooth, then which block reaches the ground first?

B A The three blocks reach the ground at the same time C

1 solution

Sam Bealing
May 20, 2016

Let the angle of inclination of the plane be $\theta$ so we have vertical force as:

$F=mg \sin(\theta)$

$F=ma \Rightarrow a=g \sin(\theta)$

Let $h$ be the height of the plane ( constant ). The vertical distance to travel is $h$ so the time taken is:

$t=\dfrac{h}{g \sin(\theta)}$

This is minimised when $\sin(\theta)$ is maximised that is when $\theta$ is as close to $90^{\circ}$ so when the plane has the steepest angle giving the answer as:

$\boxed{A}$

Moderator note:

Great explanation. Considering only one dimension allows us to simplify the considerations.

A Race on Slopes

1 solution

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