How Is Tension Calculated in a Rope Held by Two People Leaning Back?

[haloschief]

1. Two people of equal mass are holding opposite ends of a rope and lean back 15 degrees with the vertical. What is the tension in the rope exerted by each person?

This is how attempted to solve this.
So tension is created by the force of gravity from them leaning back. So I drew a force diagram sum of the tensions in the X direction should be 0. So I found the force gravity in the X direction using Tan15=T/MG which gives me MGtan15=T.

Is this the correct way to set up the problem?

Thanks

 

[6Stang7]

Looks good to me.

 

[haloschief]

Ok, so I looked at this problem again and I'm still unsure about this solution. If gravity acts only on the y direction how is it possible for it to have an x-component and solve it like I just did? Should I be taking torques into account as well as the force exerted by the ground?

 

[diazona]

Ok, so I looked at this problem again and I'm still unsure about this solution. If gravity acts only on the y direction how is it possible for it to have an x-component and solve it like I just did?

It doesn't. Assuming your y-axis is vertical, gravity doesn't have any x-component. I'm not really sold on your original solution either. (Kudos for recognizing that there was something fishy about it )

I think trying to do it with torque would be a good idea.

 

[rwisz]

for providing your approach to solving this problem. Your understanding of tension being created by the force of gravity is correct. However, it is important to note that in this scenario, the force of gravity is acting downwards and is balanced by the normal force exerted by the ground on the two people. The tension in the rope is created by the pulling force of the two people in opposite directions.

To solve this problem, you can use the concept of static equilibrium, which states that the sum of all forces acting on an object must be equal to zero for it to be in a state of rest.

First, draw a free body diagram for one of the people. The forces acting on them are the tension in the rope (T), the normal force (N) exerted by the ground, and the force of gravity (mg).

In the vertical direction, the sum of forces is equal to zero, so N + mg = 0. This means that N = -mg.

In the horizontal direction, the sum of forces is also equal to zero, so T = 0.5mg (since the two people have equal mass).

Therefore, the tension in the rope exerted by each person is 0.5mg.

So, your approach is correct in setting up the problem and using the concept of static equilibrium. Keep up the good work!