Particle on a moving wedge: Reaction Force

Question

I have been attempting to solve the following problem (my question is at the very bottom of this post)

And here is the answer for the first part

Question: Why is the reaction force $R$ not equal to $mgsin theta$? (I would think this is the case by Newton's Third Law, however, something is wrong with this logic.)

user256872 · Accepted Answer

I think you mean to say $mgcostheta$ and not $sin theta$. See below (note I only display the force of gravity):

The way we usually get that $R=mgcostheta$ is by realizing that the forces perpendicular to the incline are balanced on the block. So we have $Sigma F_perp = R-mgcostheta=0implies R=mgcostheta$.
However, this is only true when the wedge is not moving. Because the wedge is moving, $Sigma F_perp neq 0$ so you can't conclude that $R=mgcostheta$.

Particle on a moving wedge: Reaction Force

One Answer

Add your own answers!

Ask a Question