# Tension between two masses and three ropes

• jbuck
In summary, the problem involves finding T1, T2, T3, and theta for a system in equilibrium with a horizontal center string. The equations used are T1cos(angle1)-T2cos(angle2)=0 and T1sin(angle1)+T2(angle2)-mass1=0, with angle1 and angle2 representing the angles at which the three ropes connect. The FBD is drawn using the two points where the ropes connect, and not the masses. The second equation given is incorrect and further work is needed to find the correct angle for T2.
jbuck

## Homework Statement

The system is in equilibrium with the center string exactly horizontal. Find T1, T2, T3, and theta

## Homework Equations

T1cos(angle1)-T2cos(angle2)=0
T1sin(angle1)+T2(angle2)-mass1=0

## The Attempt at a Solution

Currently working on mass 1
When making free body diagrams for this problem, I think it makes more sense to use the two points at which the three ropes connect ( a and b) rather than the masses, due to the rope joining the two. I can't figure out how to incorporate this into the equations. I thought 90 degrees was correct, but that answer was illogical. I think if I'm able to find an angle for T2, the rest of the problem will fall into place.

Thank you for your help :)

#### Attachments

• Chapter 4 and 5, problem 5.pdf
24.7 KB · Views: 443
You meant that figure :

jbuck said:

## Homework Statement

The system is in equilibrium with the center string exactly horizontal. Find T1, T2, T3, and theta

## Homework Equations

T1cos(angle1)-T2cos(angle2)=0
T1sin(angle1)+T2(angle2)-mass1=0

## The Attempt at a Solution

Currently working on mass 1
When making free body diagrams for this problem, I think it makes more sense to use the two points at which the three ropes connect ( a and b) rather than the masses, due to the rope joining the two. I can't figure out how to incorporate this into the equations. I thought 90 degrees was correct, but that answer was illogical. I think if I'm able to find an angle for T2, the rest of the problem will fall into place.

Thank you for your help :)

Draw the FBD. Explain your notations. What do angle1 and angle2 mean? Your second equation is wrong. Show your work in detail.

## 1. What is the principle behind tension between two masses and three ropes?

The principle behind tension between two masses and three ropes is Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. In this case, the two masses pulling on the ropes create an equal and opposite tension force on each rope.

## 2. How is tension calculated between two masses and three ropes?

Tension can be calculated by using the equation T = F/A, where T is the tension force, F is the pulling force, and A is the cross-sectional area of the rope. In this case, the tension on each rope will be equal to the force exerted by the masses divided by the total cross-sectional area of the three ropes combined.

## 3. How does the angle of the ropes affect the tension between two masses?

The angle of the ropes does not affect the tension between two masses, as long as the ropes are parallel to each other and the masses are pulling in the same direction. However, if the angle of the ropes is not equal, the tension on each rope will be different.

## 4. What factors can affect the tension between two masses and three ropes?

The tension between two masses and three ropes can be affected by the weight of the masses, the strength and elasticity of the ropes, and any external forces acting on the system, such as friction or air resistance.

## 5. How does the tension between two masses and three ropes change if one of the ropes breaks?

If one of the ropes breaks, the tension between the two masses will decrease. This is because the total cross-sectional area of the remaining ropes will decrease, resulting in a decrease in the tension force. However, the tension on the remaining ropes will increase to compensate for the loss of the broken rope.

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