Non-uniform circular motion question

[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.

Homework Equations

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?

 

[Chewy0087]

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.

 

[neshepard]

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?

 

[Chewy0087]

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.

 

[rwisz]

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.