# Need help with a pulley and tension problem

## Homework Statement

https://imgur.com/KANlHh9 The problem and my equation for finding the tension in rope one are shown in the image above. I am stuck on finding the tension for the horizontal component of the second rope's tension and finding the angle theta

F=ma
F=T-W

## The Attempt at a Solution

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To find the tension in rope 2 I have tried to find the vertical component first, here's a run-down of what I did.

Fy=T2y-Wy
ma=T2y-mg
0=T2y-mg (since the penguin is at rest a=0)
T2y=mg
T2y=6.00kg*9.8m/s^2
T2y=58.8N

And for the horizontal component, I think the equation would go something like this?

Fx=T2x?

For angle theta I need more than one component to solve for, so at this point I can't, but if I had the x and y compenents I could just use tan^-1 adj/opp.

#### Attachments

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stevendaryl
Staff Emeritus
It is very hard to read your mathematical symbols. There's a guide for writing nicer mathematics using LaTex: https://www.physicsforums.com/help/latexhelp/

But you haven't considered all the forces in the x-direction and the y-direction. There are two objects of interest: the penguin and the pulley.

On the penguin, we have two forces: A rope pulling up, and gravity pulling down. So there is no x-component. The forces have to add to zero.

On the pulley, we have three forces: One rope pulling straight down. One rope pulling at an angle of ##30^o##. And one rope pulling at angle ##\theta##. So you need to figure out the forces in the x-direction and the forces in the y-direction separately.

• Marco Noguez
It will be very usefull to draw the Force Body Diagram of the pulley and answer the following question: What do you know about each tension force (magnitude and angle)?

haruspex