How Do You Calculate the Mass M and Support Reaction for a Balanced Beam?

In summary, using the equations for torque and equilibrium, we can determine the value of M to be 9.3 kg and the reaction of the support at C to be 164.64 N.
  • #1
Gwyddel
6
0

Homework Statement


A uniform beam AB of mass 4.5 kg is 1.6 m long. A mass of M kg is attached to end A and a mass of 3 kg is attached to end B. The beam rests horizontally in equilibirum on a smooth support at point C, where AC = 0.5 m.

Calculate the value of M and the reaction of the support at C.

Homework Equations


Torque = F * d

The Attempt at a Solution


Is this correct?

2a4wn6u.png


R = reaction of the support at C
acc. due to gravity = 9.8 ms-2

R - 9.8M - (4.5*9.8) - (3*9.8) = 0
R = 9.8M + 44.1 + 29.4
R = 9.8M + 73.5

Moments about point C.
(0.5*9.8M)-(0.3*44.1)-(29.4*1.1) = 0
4.9M - 13.23 - 32.34 = 0
4.9M = 45.57
M = 45.57/4.9
M = 9.3 kg

R = 9.8M + 73.5
R = 9.8(9.3) + 73.5
R = 164.64 N
 
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  • #2
Hi Gwyddel, welcome to PF!

I haven't checked your actual calculations in detail, but your approach and equations look great.
 

FAQ: How Do You Calculate the Mass M and Support Reaction for a Balanced Beam?

What is torque?

Torque is a measure of the twisting force applied to an object. It is calculated by multiplying the force applied to the object by the distance from the pivot point to the point where the force is applied.

What is a uniform beam?

A uniform beam is a type of structure that is evenly distributed in terms of its weight and mass. It is typically used in engineering and construction as a support structure for bridges, buildings, and other architectural designs.

How is torque applied to a uniform beam?

Torque is applied to a uniform beam by applying a force at a certain distance from the pivot point. This creates a twisting force on the beam, which is then balanced by an equal and opposite torque at the other end of the beam. This results in the beam remaining in a state of equilibrium.

What is the formula for calculating torque on a uniform beam?

The formula for calculating torque on a uniform beam is T = F x d, where T is the torque, F is the applied force, and d is the distance from the pivot point to the point where the force is applied.

What factors can affect the torque on a uniform beam?

The torque on a uniform beam can be affected by factors such as the magnitude of the applied force, the distance from the pivot point to the point where the force is applied, the weight and mass of the beam, and the type of material the beam is made of.

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