# HW: Newton's Second Law and Angles

• Aerodin
In summary: The angle is related to the acceleration due to the tension in the string, and that tension is inversely proportional to the distance between the masses.
Aerodin
[SOLVED] HW: Newton's Second Law and Angles

## Homework Statement

The system shown in the figure can be used to measure the acceleration of the system. An observer riding on the platform measures the angle (theta) that the thread supporting the light all makes with the vertical. There is no friction anywhere.

How is (theta) related to the acceleration of the system? (Mathematical/with an equation)

F=ma

## The Attempt at a Solution

Well, after working on this for at least an hour, I'm thinking that to figure out what the angle has to be I have to use the idea of drawing a free body diagram of the ball/angle part of the diagram or something. I'm really having some serious trouble doing this so any help would be awesome. Thanks!

Edit: I just figured out that if I do draw the whole free body diagram, it looks like i may be able to find how the angle is related. However, in order to do so, I need to know what the tension force of the string that the ball is on would be, and that's where I'm getting stuck.

#### Attachments

• figure.jpg
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Last edited:
So I just read a couple of other threads about similar problems as this, and I think I figured out the right answer, but I'd like someone to check it if they can...

Pretty much, I found the forces on the hanging ball in terms of x and y (like the forces in the x direct and the forces in the y direction), and then solved for theta... if this is right, then

Ax=gcos(theta)
Ay=g-gsin(theta)

Last edited:
Hey guys, I don't mean to be pesky, and I know this probably wasn't the best time to post this, but this thing is due in the morning and i just want to see if it's correct or not... thanks :)

Hard to say, while your attachment is still pending approval and we can't see it. Can you try and describe the system in words?

ohh ok sry about that. Pretty much, there are 2 masses. One is hanging off of a pully and the other is on a horizontal surface with no friction attached by that same string on the same pully. On the second mass (the one on the horizontal surface), there is a pole with a massless ball hanging. The angle that this ball is at is supposed to be related to the acceleration of the system.

Update: The picture looks like it just got approved, so that should be a lot more helpful.

Last edited:
Well, I think I figured it out, so i'll leave this as solved.

## 1. What is Newton's Second Law?

Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

## 2. How is Newton's Second Law related to angles?

Newton's Second Law can be applied to objects moving at an angle by breaking down the force vectors into their component forces in the x and y directions. The acceleration in each direction can then be calculated separately using the formula a = F/m. The resulting accelerations can be combined to determine the overall acceleration of the object.

## 3. Can Newton's Second Law be applied to rotational motion?

Yes, Newton's Second Law can be applied to rotational motion by using the concept of torque, which is the rotational equivalent of force. The formula for torque is T = rFsinθ, where r is the distance from the axis of rotation, F is the force applied, and θ is the angle between the force and the lever arm.

## 4. How does the mass of an object affect its acceleration according to Newton's Second Law?

The mass of an object is inversely proportional to its acceleration according to Newton's Second Law. This means that as the mass of an object increases, its acceleration will decrease if the force acting on it remains constant. Similarly, a decrease in mass will result in an increase in acceleration.

## 5. Is Newton's Second Law applicable to all types of motion?

Yes, Newton's Second Law is applicable to all types of motion, including linear, rotational, and projectile motion. It is a fundamental law of physics that describes the relationship between forces, mass, and acceleration.

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