Find tension using sum of torque (two strings, one beam, one box)

  • #1
dcmf
16
5
Homework Statement
The figure (Figure 1) shows a model of a crane that may be mounted on a truck. A rigid uniform horizontal bar of mass m1 = 90.0 kg and length L = 5.10 m is supported by two vertical massless strings. String A is attached at a distance d = 1.90 m from the left end of the bar and is connected to the top plate. String B is attached to the left end of the bar and is connected to the floor. An object of mass m2 = 2000 kg is supported by the crane at a distance x = 4.90 m from the left end of the bar. Throughout this problem, positive torque is counterclockwise and use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

Find TA, the tension in string A.
Relevant Equations
Tnet=ΣFlsinθ, F=mg
Here's the picture of the situation described, provided by the question.
1710544579144.png


Here's a screenshot of the work I have done.
1710544594573.png


Here's a screenshot of the submission screen.
1710544453555.png


The issue is that I have one attempt left and am not sure what I am doing wrong. Based on the hints, I feel like I'm calculating it right and using the right significant figures but it's just not accepting my answer (which is strange because usually it doesn't care about significant figures). I submitted 49363.63 and was shown the incorrect message above telling me to round to 3 significant figure so I submitted 49400 and got the same message. I feel like there's got to be something really obvious I'm missing or a concept that I am not applying. I'd really appreciate the help! Thanks in advance
 
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  • #2
You have a sign error going from eqn 2 to eqn 3 (##F_{TA}=##).
 
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  • #3
haruspex said:
You have a sign error going from eqn 2 to eqn 3 (##F_{TA}=##).
Haha I see it! Thank you so much 🤡
 

FAQ: Find tension using sum of torque (two strings, one beam, one box)

1. How do I start analyzing the problem of finding tension using the sum of torques?

Begin by identifying all the forces acting on the system, including the weight of the beam, the weight of the box, and the tensions in the two strings. Choose a pivot point to sum the torques around, typically a point where one of the unknown forces acts to simplify calculations. Use the principle that the sum of torques around any point in a system in equilibrium is zero.

2. What is the significance of choosing a pivot point when calculating torques?

Choosing a pivot point is crucial because it allows you to simplify the equations by eliminating one of the unknown forces from the torque equation. The best pivot point is often where one of the strings attaches to the beam, as the torque due to the tension in that string will be zero, reducing the number of unknowns.

3. How do I set up the torque equations for this problem?

After choosing a pivot point, calculate the torque produced by each force about that point. Torque is the product of the force and the perpendicular distance from the pivot point to the line of action of the force. Sum all the torques and set the sum equal to zero. This will give you one equation that you can solve for one of the unknown tensions.

4. How do I incorporate the weight of the beam and the box into my torque calculations?

The weight of the beam acts at its center of gravity, which is usually at its midpoint. The weight of the box acts at the point where it is placed on the beam. Calculate the torque due to these weights by multiplying each weight by its distance from the pivot point. Include these torques in your sum of torques equation.

5. How do I solve for the tensions in the two strings?

After setting up the torque equation and solving for one of the tensions, use the equilibrium condition for forces. The sum of vertical forces must be zero, so set the sum of the upward tensions equal to the total downward weight (beam plus box). This gives you a second equation, which can be solved simultaneously with the torque equation to find the tensions in both strings.

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