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## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 9

Lesson 5: Normal force and contact force

# Free body diagram with angled forces: worked example

Sal draws a free body diagram for a box held stationary against a wall with a force at an angle theta.

## Want to join the conversation?

• I don’t get it. Friction is against the direction of motion. So why is the frictional force(Ff) pointing upwards in the direction of motion instead of downwards?
• So in this scenario, the vertical component of the angled force is less than gravity. Therefore, if there was no friction, then the block would accelerate downwards. Since friction always counteracts the motion, the friction force would point upwards.

In order for the friction force to point downwards, the block would have to be trying to accelerate upwards. That would happen if the horizontal component of the angled force were greater than gravity.

Hope this helps!
• What about the equal and opposite force exerted by block which is pulling the earth?
• You are right in saying that the block is pulling up the earth, but it is really small. THis is seen through f=ma. THe forces have to be the same according to newton's 3rd law, but the mass would be far far far far far larger - the earth is very heavy, thus the acceleration is really really really really small as mass is indirectly proportional to acceleration when the force is the same. Because it is too small, it is mostly disregarded.
• whats the purpose of doing math without numbers?
• Math doesn't have to be all about numbers. Mathematicians like to generalize things so it can be applicable to all cases, when there are numbers.
• Non of those forces have to equal our right or is it just this particular set of question?
• (I know this is a year late, but I’ll answer the question anyway just in case someone else has the same one.)

The forces don’t always have to equal (even) out or add up to a net force of zero when we do these kinds of problems, but they do cancel out here.

In this problem, we’re told that the box is “held stationary”, meaning it’s at rest. Staying stationary/at rest means that the box has 0 velocity and 0 acceleration. Newton’s 2nd law says that the sum of the forces equals mass times acceleration ΣF=ma

We know the acceleration is 0m/s^2, so we can substitute it to get ΣF=m(0), which multiplies to ΣF=0.

ΣF=0 means that the sum of the forces equals 0, or that all of the forces have to add up to zero (cancel out). Even though the forces won’t always cancel out, that’s why they do here.
• At , Sal says that he doesn't draw the arrow atop F sub g because he's talking about the magnitude of the vector. Do you always need to draw the arrow? It seems like a bit of extra work for the same purpose. Thanks!
(1 vote)
• F sub g refers to the magnitude of the vector, while F sub g with an arrow refers to the whole vector (both magnitude and direction). Here the downward arrow already tells us the direction so it is fine to write only F sub g, which tells us the magnitude of the vector Fsub g. We need to draw the arrow if we want to refer to the “whole” vector and not just its magnitude.
• Think about it. If a force is there FsinQ then the friction should be exact opposite, but Sal draws it in the same direction. Why?
• Why is the normal force going sideways?
• According to Newton's 3rd law of motion, every force action (the horizontal component Fcosθ) exerted on an object (the box on the wall), has an opposite force reaction (the wall on the box) equal in magnitude and opposite in direction. This force is called the normal Force.

Hope it helps!
(1 vote)
• If Fsinθ + Ff= Fg then wouldn't there be no movement because the forces are equal?
(1 vote)
• Yes, there won't be any movement, that is why in the beginning of the video it was mentioned that the block was stationary.