How Do You Calculate Tensions in a Suspended Mass System with Different Angles?

[Fusilli_Jerry89]

a 1100N mass is suspended from a string which is supported by two poles. One side makes an angle of 70 degrees with the vertical and the other side makes an angle of 80 degrees. Find the two tensions using components.

First I say that T1sin70-T2sin80=0 bcause the x forces have to be equal, otherwise the object would sway. Secondly I saw that T1cos70+T2cos80-1100=0 because the vertical components pushing upwards must equal the weight pulling downwards in order for the system to be in equilibrium. But now I do not know what to do after i get T1cos70+T2cos80=1100.

 

[BishopUser]

You got 2 equations and 2 unknowns. Solve for a variable in one equation and plug it into the other

 

[kyle8921]

I would suggest using the equations you have derived to solve for the two tensions, T1 and T2. You can rearrange the equations to solve for either T1 or T2 and then plug that value into the other equation to solve for the remaining tension. This will give you the values for T1 and T2 in terms of the weight of the object, 1100N.

Once you have solved for T1 and T2, you can plug those values into the original equations to check if they satisfy the conditions for equilibrium. The sum of the forces in the x-direction should be equal to 0, and the sum of the forces in the y-direction should also be equal to 0. If the values you have calculated do not satisfy these conditions, then there may be a mistake in your calculations.

In addition, as a scientist, I would also suggest drawing a free-body diagram of the system to better visualize the forces acting on the object. This can help in understanding the problem and deriving the appropriate equations. It is also important to keep track of the directions of the forces and the corresponding angles, as any mistakes in these can lead to incorrect solutions. Overall, it is important to approach the problem systematically and carefully to ensure accurate results.