# Non-uniform circular motion question

• neshepard
In summary, an object of mass 0.500kg is suspended from the ceiling of an accelerating truck with an acceleration of 3.00m/s^2. To find the angle θ of the string with the vertical and the tension T in the string, the equations mgsinθ=ma and mgcosθ=T are used. However, it is important to note that mg cannot be bigger than T, as it supports the weight of the mass in the upward direction and also acts against the acceleration of the lorry. Drawing a diagram can help to visualize the forces at play.
neshepard

## Homework Statement

An object of mass m=.500kg is suspended from the ceiling of an accelerating truck. Taking a=3.00m/s^2 find the angle θ that the string makes with the vertical and the tension T in the string.

## The Attempt at a Solution

mgsinθ=ma => sinθ=1.5/4.9 =>θ=17.8

mgcosθ=T => T=4.67N

But alas this is incorrect. Where did I fail?

Be careful with mg & T.

For example, in your second equation, you're implying that mg is bigger than T, think about why that can't be true.

Your resolving is fine though, just think about the mg & T, if you need more help just ask.

Edit: I'm also not sure what this has to do with circular motion.

As to why circular motion...got me. It's in that chapter in the book.

With T and mg, wouldn't mg be bigger since due to acceleration? If I reverse my equation and have T bigger, is it mg-Tcosθ? and why?

The reverse is correct. Draw yourself a diagram and label all of the forces.

The string has to both support the weight of the mass (mg) in the upward direction, but it also acts against the acceleration of the lorry which pushes the mass towards the back of the lorry. Because the net force on it is 0, right? Anyway, I think the diagram should help.

Your attempt at a solution is incorrect because you have assumed that the object is in uniform circular motion, which is not the case here. In uniform circular motion, the acceleration is always perpendicular to the velocity, but in this scenario, the acceleration of the truck is not perpendicular to the string. This means that the tension in the string is not equal to the weight of the object, and the angle θ cannot be determined using the equations for uniform circular motion.

To solve this problem, we need to consider the forces acting on the object. The object has a weight of mg acting downwards, and a tension force T acting upwards along the string. In addition, there is also an acceleration force acting on the object due to the truck's acceleration, which we can represent as ma.

Using Newton's Second Law, we can write the following equations:

ΣFy = T - mgcosθ = ma

ΣFx = mgsinθ = 0

From the second equation, we can see that sinθ = 0, which means that θ = 0. This makes sense, as the object is not moving horizontally and the string is perpendicular to the ceiling.

Substituting this value of θ into the first equation, we get T - mg = ma. Solving for T, we get T = mg + ma. Plugging in the given values, we get T = (0.500kg)(9.8m/s^2 + 3.00m/s^2) = 6.90N.

Therefore, the angle θ is 0 degrees and the tension in the string is 6.90N. This solution takes into account the non-uniform acceleration of the truck and the forces acting on the object.

## What is non-uniform circular motion?

Non-uniform circular motion is the movement of an object in a circular path where the speed or velocity is constantly changing.

## What causes non-uniform circular motion?

Non-uniform circular motion is caused by a combination of centripetal force, which keeps the object moving in a circular path, and tangential force, which changes the speed or velocity of the object.

## What is the difference between non-uniform circular motion and uniform circular motion?

Uniform circular motion is when an object moves in a circular path at a constant speed, while non-uniform circular motion is when the speed or velocity of the object is constantly changing.

## How is non-uniform circular motion related to acceleration?

Non-uniform circular motion involves acceleration because the velocity of the object is constantly changing, meaning there is a change in speed and/or direction, which is the definition of acceleration.

## What are some real-life examples of non-uniform circular motion?

Some examples of non-uniform circular motion are a car going around a bend, a roller coaster going through loops, and a satellite orbiting the Earth. These all involve an object moving in a circular path with changing speed or velocity.

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