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.