# Need help with a pulley and tension problem

• Scott McKinnon
In summary, the problem is trying to find the tension in the horizontal component of the second rope's tension and finding the angle theta.
Scott McKinnon

## 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

[/B]
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

• KANlHh9.jpg
49.5 KB · Views: 1,673
Last edited by a moderator:
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)?

The problem I have with reading your attempt is that you have not defined your variables. Which are you thinking of as rope 2?
If you mean the one at an angle then, as @Marco Noguez hints, your mistake is thinking of that tension as acting directly on the penguin. That rope is not attached to the penguin. Treat the pulley and penguin separately.

## 1. What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a grooved rim and a rope or cable wrapped around it. It is used to change the direction of a force and make it easier to lift or move heavy objects. When a force is applied to one end of the rope, the object on the other end of the rope will move in the opposite direction.

## 2. How do you calculate the tension in a pulley system?

The tension in a pulley system can be calculated by using the formula T = (2W)/n, where T is the tension, W is the weight of the load being lifted, and n is the number of supporting ropes or cables. This formula assumes that the pulley is frictionless and all ropes are equally taut.

## 3. What factors affect the tension in a pulley system?

The tension in a pulley system is affected by the weight of the load being lifted, the number of supporting ropes or cables, and the angle at which the ropes are pulling on the pulley. Other factors such as friction and the weight of the pulley itself may also affect the tension.

## 4. How does the number of pulleys affect the tension in a system?

The number of pulleys in a system does not affect the tension, but it can make it easier to lift or move heavy objects. The more pulleys used, the less force is needed to lift the load. However, the distance that the rope must be pulled will increase as well.

## 5. What are some common uses for pulleys in everyday life?

Pulleys are commonly used in elevators, cranes, and construction equipment to lift and move heavy objects. They are also used in exercise equipment, such as weight machines, to provide resistance. In everyday life, pulleys can be found in window blinds, clotheslines, and flagpoles.

Replies
2
Views
2K
Replies
8
Views
974
Replies
9
Views
4K
Replies
18
Views
575
Replies
12
Views
2K
Replies
22
Views
4K
Replies
5
Views
3K
Replies
2
Views
1K
Replies
1
Views
2K
Replies
7
Views
2K