# Problem in wedge constraint [closed]

My teacher told all this (u can see in picture)

Here both accelerations have component in -j direction, then why do we say that they cancel out? [X-axis is surface of wedge]

I have problem in photo 2

• your hand writing is hard to read and there are abbreviations, would you mind typing the full text ? what is "-j direction" ? What is the relationship between firist pic and second one ? Commented May 4, 2021 at 15:47
• i think u know that -j is negative y direction and i have already told x direction, so u can see what will be y axis on the point of mass m Commented May 4, 2021 at 16:31

The answer is quite simple. In the constrained motion problems given above, the main constraint is that both surfaces must be in contact with each other. This is possible only if the component of acceleration of the two bodies in the direction perpendicular to that of motion is equal both in magnitude and direction i.e. the relative acceleration of the two bodies in the direction perpendicular to motion must be zero.

Here both accelerations have component in -j direction, then why do we say that they cancel out? [X-axis is surface of wedge]

The discussion here is on the relative acceleration of the two bodies in the direction perpendicular to that of motion.

Relative acceleration is given by:-$$\vec{a_{2/1}}=\vec{a_{2}}-\vec{a_{1}}$$

So, if the component of acceleration of the two bodies in the direction perpendicular to motion is equal both in magnitude and direction, we can expect their difference to be zero which is exactly your relative acceleration of the two bodies in the direction perpendicular to motion. Of course, the two accelerations do not cancel out each other as they are in the same direction!!

Hope it helps you.

• Anyway thanks, I really felt like a fool after reading this Commented May 4, 2021 at 16:43
• @Gaurav Could you please accept the answer as well if it really helped you. It feels good to know that my answer helped someone :) :) Commented May 4, 2021 at 16:47