Static Equilibrium incorporating torque

In summary: Setting these equal gives you the answer.In summary, using the given information of a 60 kg man hanging one meter from the end of an 8 m, 100 kg beam supported by a frictionless pin, with a steel cable attached to the end of the beam making a 35 degree angle with the horizontal, the tension in the cable can be calculated by using the equations of T=Fd and the conditions of net force and net torque being equal to 0. By setting the torque from the weight of the beam and man equal to the torque of the tension in the cable, the equation T x 8 sin 35 = 4 x Wp + 7 x Wm can be used to solve for the tension
  • #1
EV33
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Homework Statement



A 60 kg man hangs one meter from the end of an 8 m, 100 kg beam. A steel cable is attached to the end of the beam near the man, and the opposite end is supported by a frictionless pin (or a hinge). The system is originally at rest. The cable makes a 35 degree angle between the horizontal and the hypotenuse.
Find the tension in the cable.



Homework Equations



T=Fd

Net Force=0
Net Torque=0

The Attempt at a Solution



I draw my free body diagram and get the weight force of the steel rod being exerted at 4 m. I get the hanging man’s normal force at 7 m. I get a tension force at 35 degrees on one end, and then I get a vertical and horizontal normal force from the pin on the other side.

Horizontal forces
Pin(x)-Cable(x)=0

Vertical forces
Pin(y) + Cable(y) -Beam- Man=0

I am having trouble incorporating torque into this problem and I know I need to. Where should I place my reference frame to find torque?
 
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  • #2
Take moments about the pin/hinge.
If the pin is to the left of the man and the cable to the right
clockwise: the man and the weight of the beam
counterclockwise: moment of the tension about the pin
 
  • #3
ok I just retried this problem...

I added the torque's of the rod and the man, and figured the vertical component of the tension in the cable should be equal to the torque.


(4)(100)(9.81)+7(65)(9.81)=8387.55=Torque

then to get the tension in the actual cable I did...

8387.55/sin(35)=14623.24717=tenion

This numbers seem pretty high to me. Is this wrong? If sowhere did I go wrong.

Thank you.
 
  • #4
The first part is correct. (Is the man 60 or 65 kg?)
The moment(torque) of the tension about the pin is given by the tension T in the cabel times its perpendicular distance from the pin.
If you draw the triangle (rod(8m), cable, 35deg) you will see that this distance is given by 8 sin (35)
If you equate the the two torques now you should get the answer.
 
  • #5
(4)(100)(9.81)+7(60)(9.81)=8044.2=Torque on the pin
Torque exerted by cable=8F=8044.2
F=1005.525

I figured that the Force involved was the vertical component so I divided it by sin(35) to get the tension in the cable.

Tension(cable)=1753.079?

I am not sure what you were saying to do with the triangle. Is this what you were saying?
 
  • #6
The torque from the steel cable is the tension in it (T) multiplied by the perpendicular distance (OP) of the line of force from the pin. Here's how it looks.
planckmoments2.png

The perpendicular distance is r in the diagram and is 8 sin 35

You have the correct clockwise torque
4 x Wp + 7 x Wm [weight of beam and man]
This is balanced by the torque of the tension, T, of the cable, and this is
T x OP = T x 8 sin 35
 

Related to Static Equilibrium incorporating torque

1. What is static equilibrium?

Static equilibrium refers to the state of an object or system where all forces acting on it are balanced, resulting in a stable and motionless state.

2. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied by the distance from the axis of rotation.

3. How is torque related to static equilibrium?

In order for an object to be in static equilibrium, the sum of all torques acting on the object must be equal to zero. This means that the clockwise and counterclockwise torques must balance each other out.

4. What factors affect the torque on an object?

The magnitude of torque on an object depends on the force applied, the distance from the axis of rotation, and the angle between the force and the lever arm. Increasing any of these factors will result in an increase in torque.

5. How can I apply the concept of static equilibrium and torque in real life?

Static equilibrium and torque are important concepts in many fields, including engineering, physics, and biomechanics. They are used to design stable structures, analyze forces acting on objects, and understand the mechanics of human movement.

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