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## High school physics

### Course: High school physics>Unit 3

Lesson 6: Angled forces

Sal explains how to draw free body diagrams when forces are applied at an angle. How to find horizontal and vertical components of an angled force using trigonometry.

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• In this video the 20N force is splitted into 2 forces of 10N and 10√3N respectively, but 10+10√3>20, how is that even possible?
• It is because when you split forces you have to use the Pythagorean theorem, or hypotenuse^2 = side^2 + side^2. In this case, the hypotenuse is 20 N, and the two sides are 10 N and 10sqrt(3).
If you square the hypotenuse, you get 20^2, which equals 400 N.
10^2 + (10sqrt(3))^2 = 100 + 300, which equals 400 N, or the hypotenuse squared.

Therefore, those are the two components of the force, proven by the Pythagorean theorem.

Think of it this way: if you have a triangle with two sides of length 3 and 4, the hypotenuse does not have to be 3 + 4 = 7; in fact, it will be 5. This is because 3^2 + 4^2 = 5^2 (9 + 16 = 25).
• At , is it true that, in this example, the normal force is also the "Newton Third Law Partner Force" of the gravity?
• Nope. Action and reaction forces operate on different objects, not the same object. The reaction force to the normal force the surface exerts on the object (up) is the normal force the object exerts on the surface (down). The reaction force of the gravity earth exerts on the object (down) is the gravity the object exerts on earth (up). The reason earth isn’t affected much by this gravity is that its mass is much much greater, so its acceleration is negligible.

So to sum up, Action and reaction forces operate on different objects and are the same type of force (reaction force of normal force is still normal force, reaction force of gravity is still gravity, reaction force of friction is still friction). In addition to that is Newtons third law: magnitude, direction, orientation, etc.
• why isn't there a force to the left as the x-component? kind of like the y component going down?
• As Sal mentioned at the start of the video, the surface the body is rested on is a flat and FRICTIONLESS surface, and thus, in this case, there won't be any friction working against the motion of the body (or a force to the left of the x-component as you said). Hope this helps, thanks.
• are free body diagrams and force diagrams the same thing? Why did we have to use trig when we could just use Pythagorean theorem?
• Both legs of the right triangle were unknown so you couldn't have solved for one of the sides.
• At how come Sal writes positive 10N for both Fn and Fg? Wouldn't one of them have to be negative 10N so that they can balance out?
• He uses arrows for direction, so the negative for Fg is implied.
• can include tan theta here? somehow?
because sinA/cosA=tanA
• If you want to find the horizontal and vertical forces, given the force and angle, you would only need to use sin and cos.
• at , why is the force going up 10 + 10*sqrt(3), but the force going down is 2 different forces: 10, and sqrt(3)?
(1 vote)
• The force that is pulling the box down is the force of gravity, 10 N, and the vertical component of the angled force, 10sqrt(3) N. Thus, the total force pulling down on the box is 10 + 10sqrt(3) N. The force going up, the normal force, completely counteracts the force pulling down, so the normal force is also 10 + 10sqrt(3) N. Hope this helps.
• why normal force is equal to sum of horizontal component and vertical component of forces in the video at
(1 vote)
• Normal force, in this case, is the support force that is acting vertically-upwards on the body. Since it is given that the body has a vertical acceleration = 0m/s2, therefore, the object has net vertical force = 0N. Since there are 2 types of forces being exerted on the body (Weight force, Push force), to have a vertical net force = 0N; there would also be a force acting vertically-upwards that can cancel out these 2 forces. That force is the Normal force (Support force) and to cancel out, the Normal force = Weight force + Push force. Hope this helps, thanks.
• On his free-body diagram at the end, couldn't you have combined the two downward forces to get 10+10sqrt3 N? He did so for the up components.
(1 vote)
• Technically, you can, but since those 2 values belong to different forces, you have to separate them to show that this value is force of gravity and this value is the angled force's component.

You only combine them when trying to solve something using those values since they're in the same direction. In the FBD though, it's best to leave them be so you can see what forces are acting on the object.
(1 vote)
• why doesn't normal force have an opposite force pushing down?

do we count the vertical component of gravitational force as the opposite force to normal? If so, is that because normal force is a function of gravity, so therefore the gravitational force is what has the opposite to the normal force?
(1 vote)
• The harder gravity pushes down, the harder the object is pressed into the earth (assuming we're on earth), so the harder the normal force will push back.
(1 vote)