Gravitational Torque HW: M1,M2,X1,X2,g | Calculate T

In summary, the magnitude of the torque about the point where the beam is bolted in place is 11.9kNm.
  • #1
Blistex
2
0

Homework Statement



A 4.0m long, 500kg steel beam extends horizontally from where it has been bolted to the framework of a new building under construction. A 70kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the point where the beam is bolted in place?

M1 = 500kg
M2= 570kg
X1 = 0m
X2 = 4m
g = 9.8 m/s2

Homework Equations



T = Mgxcm

Where Mg is the net gravitational force on the object and Xcm is the moment arm between the rotational axis and the center of mass.

The Attempt at a Solution



I thought this problem would quite simple but I think there might be an error in my reasoning.

I start by calculating the center of mass. {(500kg)(0m) + (570kg)(4m)}/1070kg = 2.13m
So the CM is 2.13 from the fulcrum.

Next I substitute the given values into the equation. T = (500kg + 70kg)(9.8m/s2)(2.13m) = 11902NM or 11.9k Nm.
This should be the torque about the fulcrum.

Thanks for the help :tongue: the book says 12.5k Nm. So far it's been pretty spot on this far.
 
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  • #2
Welcome to PF!

Hi Blistex! Welcome to PF! :smile:
Blistex said:
A 4.0m long, 500kg steel beam extends horizontally from where it has been bolted to the framework of a new building under construction. A 70kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the point where the beam is bolted in place?
…
M1 = 500kg
M2= 570kg

erm :redface: …

where did 570 come from? :wink:​

(and anyway, you don't need to find the centre of mass, just find each torque separately, and add! :smile:)
 
  • #3
Thank Tim!

Given Tgrav = Mgxcm

I summed the individuals particles that had torque on the object. I.e only the worker. which amounted to dsin(x)*m*g = -2744Nm

The other side of the equation asks for the mass relative to the center of rotation, that's where my miscalculation entered. Whereas the center of mass is simply 4m/2, the center of the length of the beam. I had thought the weight of the worker would cause the CM to shift farther towards the worker. I guess that's what relative meant. After plugging in the rest of the variables I was able to solve it.

Thanks for your help.
 

1. What is gravitational torque?

Gravitational torque is a measure of the rotational force exerted on an object due to the gravitational attraction of another object. It is calculated by multiplying the mass of the object (M1) by the distance from the center of mass (X1) to the center of rotation, and the mass of the attracting object (M2) by the distance from the center of mass (X2) to the center of rotation, and then multiplying by the acceleration due to gravity (g).

2. How is gravitational torque calculated?

To calculate gravitational torque, you will need to know the masses of the two objects (M1 and M2), the distances from their centers of mass to the center of rotation (X1 and X2), and the acceleration due to gravity (g). The formula for gravitational torque is T = M1*X1*g + M2*X2*g.

3. What units are used to measure gravitational torque?

Gravitational torque is typically measured in newton-meters (Nm) or foot-pounds (ft-lb) in the metric and imperial systems, respectively. These units represent a measure of force multiplied by a measure of distance.

4. How does gravitational torque affect objects?

Gravitational torque causes objects to rotate around a fixed axis, similar to how a force causes objects to move in a straight line. The magnitude of the torque depends on the masses and distances of the objects involved, and the direction of the torque is determined by the direction of the gravitational force between the objects.

5. Can gravitational torque be applied to non-rotating objects?

Yes, gravitational torque can still be calculated for non-rotating objects, although it may not have any practical significance. In this case, the torque would be equal to zero since there is no rotation occurring. However, understanding gravitational torque is still important for understanding the forces at play in a system of objects.

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