# Determine the mass of an object using the angle in the system

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I have a project from my Mechanics class which consist on building the system on the picture. It has a spring, cable and a protractor. I have to do an approximation of the mass and weight of the object that is put in the platform by using the geometry of the system and statics concepts.

The ultimate goal is to create an Excel Workbook in order to to do the necessary calculations for the weight where I only need to put the measure of the α angle to get an approximation of the object weight.

Fx = 0 and Fy = 0 but I have to find a way to determine the tension from the left side in terms of the α and the force of the string in terms of its constante and the angle.

Which statics and geometry concepts should I apply to get a good approximation of the mass and weight of the object?

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CWatters
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I would suggest you make sure you understand how Newton's second law is applied in different directions in statics problems.

ΣFx=0 and ΣFy=0 are certainly true, but, as you note, there are forces you don’t know. There are other similar equations, which I feel certain you know, which must also be true and may prove more useful.

I would suggest you make sure you understand how Newton's second law is applied in different directions in statics problems.

I would use statics equation in x and y but the tension on the the left side is an unknown force and the spring force also.
How should I relate the angle α with the tension on the left and the spring force?

The picture contains a free body diagram I did.

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ΣFx=0 and ΣFy=0 are certainly true, but, as you note, there are forces you don’t know. There are other similar equations, which I feel certain you know, which must also be true and may prove more useful.

Are you thinking about using Hooke's Law on the right side? I was thinking about calculating the spring constant in lab and find a way to determine its force in terms of k, however I can´t think of a way to "connect" the angle α in both sides of the system.

haruspex
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Are you thinking about using Hooke's Law on the right side? I was thinking about calculating the spring constant in lab and find a way to determine its force in terms of k, however I can´t think of a way to "connect" the angle α in both sides of the system.
You can measure AB and BC. Finding AC from α is fairly elementary geometry.

Are you thinking about using Hooke's Law on the right side? I was thinking about calculating the spring constant in lab and find a way to determine its force in terms of k, however I can´t think of a way to "connect" the angle α in both sides of the system.

You will certainly have to use Hooke’s law, but that wasn’t the hint. You are using a protractor to measure angle, as in rotation. Yes the sum of the forces equals 0, but what can you say about rotational motion?

• CWatters
You will certainly have to use Hooke’s law, but that wasn’t the hint. You are using a protractor to measure angle, as in rotation. Yes the sum of the forces equals 0, but what can you say about rotational motion?
You will certainly have to use Hooke’s law, but that wasn’t the hint. You are using a protractor to measure angle, as in rotation. Yes the sum of the forces equals 0, but what can you say about rotational motion?

Rotational motion is restricted and therefore ∑Mo = 0 in any point in the system.

haruspex
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2020 Award
Which formulas would you use to calculate AB and BC knowing just α angle?
The cosine rule.

Rotational motion is restricted and therefore ∑Mo = 0 in any point in the system.

I will assume that by M0 you are indicating torque. Correct. Pick the appropriate pivot, and you will find you can express all of the torques as a function of the angle on the protractor with no unknown forces of constraint. Set them equal to 0 and solve.

I will assume that by M0 you are indicating torque. Correct. Pick the appropriate pivot, and you will find you can express all of the torques as a function of the angle on the protractor with no unknown forces of constraint. Set them equal to 0 and solve.

Yes, I was referring to torque. Would it apply to the spring force? I´m sure I need to calculate the spring constant first. If I choose B as pivote then tension on the left side would be eliminated and I would have to work with the weight and the y component of the spring force.

Which would be the best way to express the spring force as a function of α?

The cosine rule.

That certainly would be useful for the length of each side. However, how can i use the geometry to determine forces?

Yes, I was referring to torque. Would it apply to the spring force? I´m sure I need to calculate the spring constant first. If I choose B as pivote then tension on the left side would be eliminated and I would have to work with the weight and the y component of the spring force.

Which would be the best way to express the spring force as a function of α?

The y component of the spring force? Think again. What is the definition of torque? Also, I don’t think you calculate the spring constant from the picture. The spring constant should be a known input to the calculation.

The y component of the spring force? Think again. What is the definition of torque? Also, I don’t think you calculate the spring constant from the picture. The spring constant should be a known input to the calculation.

Moment of a force (torque) measures the tendency of a force F to make a rigid body rotate about a fixed axis directed along a point. I have to find an appropriate pivote point in the system to delete unknown forces.

MO = rFsinθ = Fd

The moment (torque) Mb of the force T about B is 0 since this force passes through B.

The spring constant will be calculated in lab and therefore it will be a known input.

haruspex