Find Maximum mass with the principles of torque and rotational equilibrium

In summary, the conversation is about a physics problem involving a beam that is free to pivot and a cable supporting it. The goal is to determine the maximum mass a person can have before the cable snaps. The correct answer is 79.3 kilograms, which can be found by summing the forces in the Y direction and considering the angle of the cable relative to the beam.
  • #1
Leanna.Agahi
1
0
I need help with this physics problem! Please help I'm completely stuck.

A beam 3m long is free to pivot up and down about the end attached to a wall. The mass of the beam is 25 kg and the cable supporting the beam can support a maximum force of 1800 N. What is the maximum mass that a man standing on the end can have before he snaps the cable. The angle of elevation between the cable and the beam is 30 degrees.
?
I tried converting the 25 kg to Newtons, therefore getting me 245N and subtracting that from the 1800 (which I thought would be the easy way) and then dividing by 9.8 to get the mass in kg, but that ended up being incorrect.

The correct asnwer is 79.3 Kilograms, but I would enjoy to know how to get to that conclusion.
 
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  • #2
You are almost correct except one thing, you forgot the angle of the cable relative to the beam.

redo your equation by summing the forces in the Y direction (1800N is not in the Y direction)
 

FAQ: Find Maximum mass with the principles of torque and rotational equilibrium

1. How do you calculate torque?

Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation. The formula for torque is T = F x d, where T is torque, F is force, and d is distance.

2. What is rotational equilibrium?

Rotational equilibrium is a state in which an object is not rotating, or is rotating at a constant speed, with no net torque acting on it. This means that the clockwise and counterclockwise torques on the object are equal and cancel each other out.

3. How can you find the maximum mass with the principles of torque and rotational equilibrium?

To find the maximum mass with the principles of torque and rotational equilibrium, you must first determine the distance from the axis of rotation at which the mass will be placed. Then, using the formula T = F x d, you can calculate the maximum force that the mass can exert without causing the object to rotate. Finally, by dividing this force by the acceleration due to gravity (9.8 m/s^2), you can find the maximum mass that can be supported at that distance without causing rotational equilibrium to be disrupted.

4. Can the maximum mass change depending on the distance from the axis of rotation?

Yes, the maximum mass can change depending on the distance from the axis of rotation. This is because the torque increases as the distance from the axis of rotation increases. Therefore, a greater force can be applied at a greater distance without causing rotational equilibrium to be disrupted.

5. What are some real-life applications of using torque and rotational equilibrium?

Torque and rotational equilibrium are used in many real-life applications, such as balancing objects on a seesaw, tightening bolts with a wrench, and designing bridges and other structures to withstand forces and maintain stability. They are also important in understanding the mechanics of sports movements, such as swinging a baseball bat or hitting a golf ball.

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