Mass suspended by 3 ropes (midterm practice)

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In summary, a 100kg mass is suspended by three ropes attached at different points. The ropes connect at a specific point and the mass is attached there as well. The question asks for the tension in one of the ropes. To solve this problem, it is recommended to draw a picture and construct a free-body diagram. The answer to the question is 810N.
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thesunken
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A 100kg mass is supended by 3 ropes. one rope is attached at a point 1m[itex]\hat{x}[/itex] + 1m[itex]\hat{y}[/itex], one is attached at 1m[itex]\hat{x}[/itex] - 1m[itex]\hat{y}[/itex] and one is attached at -4m[itex]\hat{x}[/itex]. The three ropes all connect at -1m[itex]\hat{z}[/itex], at which point the mass is attached. What is the tension T in the rope attached at -4m[itex]\hat{x}[/itex]?

I found this problem in my midterm study sheet, but I have no idea how to solve it.
I only know the answer is supposed to be 810N but I don't understand how to get there. Thanks
 
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First draw a picture, then construct the free-body diagram.

ehild
 

FAQ: Mass suspended by 3 ropes (midterm practice)

What is the concept behind a mass suspended by 3 ropes?

The concept behind a mass suspended by 3 ropes is that the mass is being held in equilibrium by the tension forces created by the three ropes. This is known as static equilibrium, where the sum of all forces acting on the mass is equal to zero.

How do you calculate the tension forces in each rope?

To calculate the tension forces in each rope, you can use the equation T = mg, where T is the tension force, m is the mass of the object, and g is the acceleration due to gravity (9.8 m/s^2). You can also use the equations of static equilibrium, which state that the sum of all forces in the x direction and the sum of all forces in the y direction must equal zero.

What factors can affect the tension forces in each rope?

The tension forces in each rope can be affected by the mass of the object, the angle of each rope with respect to the horizontal, and the length of each rope. Additionally, any external forces acting on the mass can also impact the tension forces in the ropes.

How does the angle of each rope affect the tension forces?

The angle of each rope with respect to the horizontal can have a significant impact on the tension forces. As the angle increases, the tension force in that rope will also increase. This is because the force of gravity acting on the mass is now being split into two components, one parallel to the rope and one perpendicular. The parallel component contributes to the tension force in that rope.

Can you determine the mass of the object using this setup?

Yes, the mass of the object can be determined by using the equations of static equilibrium. By measuring the angles and lengths of the ropes, and calculating the tension forces in each rope, you can then solve for the mass of the object. However, it is important to note that this method assumes ideal conditions and may not be completely accurate in real-world scenarios.

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