Solving Wheel & Mass Problem - Brandon Seeking Help

[trojsi]

Hi folks,
In a tutorial I was given this problem on which I've been trying to solve these last 2 day with non luck. The Problem is attached with a diagram. I tried to take the torque as being T=mg-mR$$\alpha^{2}$$ but it was all in vein. Any help would be much appreciated

Thanks

Brandon

 

[SteamKing]

Clearly, mg is a force. What else do you need to convert this term into a torque?

 

[trojsi]

the thing is that I need to derive an equation to the one given and explain the steps involved, I will try to upload a more clear copy of the question.

 

[trojsi]

Yeah, youre right, I was mistaken, torque is not a force, sry. Any Clues please?

 

[paranormal]

Hi Brandon,

I understand your frustration with this problem. It can be difficult to solve problems like this, but don't give up! Let's take a look at the information given and see if we can come up with a solution together.

First, let's define the variables in this problem. T represents the torque, m represents the mass, g is the acceleration due to gravity, R is the radius of the wheel, and alpha is the angular acceleration.

Now, let's think about what forces are acting on the system. We have the force of gravity pulling down on the mass, and we also have the force of the wheel pushing up on the mass. These forces are balanced when the system is in equilibrium.

To find the torque, we need to consider the distance from the pivot point (the center of the wheel) to where the forces are acting. The force of gravity acts at the center of mass of the object, which is a distance R/2 from the pivot point. The force of the wheel acts at a distance of R from the pivot point.

Using this information, we can set up an equation for the torque:

T = (m*g*(R/2)) - (m*R*alpha^2)

Now, we can plug in the values given in the problem and solve for alpha:

T = (2kg*9.8m/s^2*(0.1m/2)) - (2kg*0.1m*alpha^2)

T = 0.98Nm - 0.2kg*m*alpha^2

Solving for alpha, we get:

alpha = √(0.98Nm/0.2kg*m) = 2.21 rad/s^2

I hope this helps you in solving the problem. Remember to always break down the problem into smaller parts and consider all the forces and distances involved. Good luck!