Question on torques. quick one.

In summary, the conversation discusses finding the torque and ratio of masses in a system in equilibrium. The initial attempt at a solution shows a ratio of 4M : 1m, but the correct answer is said to be 5. Another method is then suggested, which involves finding the center of mass for the system. The final conclusion is that the ratio of M to m is 1:4.
  • #1
RoboNerd
410
11

Homework Statement


Untitled 3.jpg


Homework Equations


ok, I thought that the torque from the mass 'm' would be equal to torque from mass 'M'

The Attempt at a Solution


I wrote down:

m * g * (d/4) = M * g * d

(m/4) = M

m = 4M

Thus, the ratio is 4M : 1 m, which gives answer 1.

However, the solutions say that the answer is 5.

Could anyone please weigh in, and thanks in advance for the help!
 
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  • #2
I agree with your answer.
 
  • #3
RoboNerd said:
Thus, the ratio is 4M : 1 m
No, you have shown 4M=1m. Think of M and m as numbers there. What is M/m?
 
  • #4
ahh 1/4. Right, thanks!
 
  • #5
I have another method,
For the system to be in equilibrium the centre of mass should lie exactly on the pivot.

Assume the pivot to be at (0,0)
assume M to be at (d,0)
assume m to be at (-d/4 ,0)
Applying the formula of center of mass
x c.o.m. = (m(-d/4) +Md)/(m+M) = 0

Md = md/4
M:m=1:4
 
  • Like
Likes CWatters and RoboNerd
  • #6
That sir is an awesome and time-saving method! Thanks a lot! Everyone thanks!
 

Related to Question on torques. quick one.

1. What is a torque?

A torque is a measure of the force that causes an object to rotate around an axis or pivot point. It is a product of the magnitude of the force and the distance between the point of application and the axis of rotation.

2. How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance from the point of application to the axis of rotation. Mathematically, it can be expressed as T = F x d, where T is torque, F is force, and d is distance.

3. What are some common units of torque?

The SI unit for torque is Newton-meters (Nm), but it can also be expressed in foot-pounds (ft-lb) or inch-pounds (in-lb).

4. How does torque affect rotational motion?

Torque is directly proportional to angular acceleration, meaning that the greater the torque applied to an object, the faster it will rotate. It also determines the direction of rotation, with clockwise torque causing clockwise rotation and counterclockwise torque causing counterclockwise rotation.

5. What are some practical applications of torque?

Torque is important in many everyday activities, such as opening a door or using a wrench to tighten a bolt. It is also crucial in mechanical engineering, as it is used to design and analyze machines and structures that involve rotational motion, such as engines, turbines, and gears.

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