# Block held by a rope on an incline

• trolling
In summary: I just wonder how it can be realized. Imagine you tilt a table and put a book on it, you attach a string to the book, - how do you manage to pull the string horizontally? Drilling a hole through the table? :smile:If you attach a string to an object on a tilted table at a 90 degree angle to the table, the pull will be horizontal. This is the same concept as the block on an incline with a string pulling horizontally. The string is attached to the object at a 90 degree angle, making the force of the string pull horizontal.

## Homework Statement

A block with mass m1 = 9.4 kg is on an incline with an angle θ = 31.0° with respect to the horizontal. There is also a massless rope that pulls horizontally to prevent the block from moving. What is the tension in the rope?

## Homework Equations

Fg = m*g
Fg,x = m*g*sin 31 = Tx (?)
Fg,y = m*g*cos 31 = Fn
Ff = u*Fg,y

## The Attempt at a Solution

Fg = 9.4kg*9.8m/s^2 = 92.12N
Fg,x = Tx(?) = 92.12N * cos 31 = 84.156N
Fg,y = Fn = 92.12N * sin 31 = 37.469N
Ff = u * Fn

I had a value for the coefficient of static friction, but that was for a system with a spring (.292), so I don't think that'll work here. I also have one for kinetic friction (.212), but that might not apply here. I'm a little unsure in finding the tension in the x-direction, since I'm pretty sure if I can find that, I can find the overall tension using Tx/cos31. But after that, I'm stuck.

Start by making a free body diagram. If you aren't given any information about the coefficient of friction in the question, why to deal with it? ;)

The body is in rest. So the tension must be balanced by one of the components of the weight.

Pranav-Arora said:
Start by making a free body diagram. If you aren't given any information about the coefficient of friction in the question, why to deal with it? ;)

The body is in rest. So the tension must be balanced by one of the components of the weight.

Ok, I have a FBD set up, but since this site won't let me post it, I can't show it. Looking at your last statement, I'm guessing that the x-component of the weight (37.469N) MIGHT be equal to the x-component of the tension. I then used that component to divide by cos 31° to get the overall tension, which I got to be 43.713N; however, my solutions box won't accept that as an answer.

(see attachment)
The tension on the block acts as shown in the attachment, not in the x-direction. As i already said, a component of weight balances tension. Your job is to find that component.

#### Attachments

• incl.jpg
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Trolling, could you please copy the full text of the problem? The static friction has to be taken into account if it was given for the same slope and block. Also, is it really said that the string pulls horizontally to prevent the block from sliding? That is rather impossible. The block can be pulled by a string along the slope, as in Pranav-Arora's picture.
When you set up a coordinate system, indicate the direction of the axes. Here, the x-axis is parallel to the slope, the y-axis is perpendicular to it.

You can upload pictures up to 300 KB. Make a jpg file of your drawing, click on "Go Advanced" then "Manage Attachments". Or you can upload files to http://imageshack.us/ and give the URL.

ehild

ehild said:
You can upload pictures up to 300 KB. Make a jpg file of your drawing, click on "Go Advanced" then "Manage Attachments". Or you can upload files to http://imageshack.us/ and give the URL.

If i remember correctly, he cannot post links until he has a post count of 10.

Pranav-Arora said:
(see attachment)
The tension on the block acts as shown in the attachment, not in the x-direction. As i already said, a component of weight balances tension. Your job is to find that component.

Err According to the OP the problem says the rope is horizontal so the tension in it does act in the x-direction.

ehild said:
Trolling, could you please copy the full text of the problem? The static friction has to be taken into account if it was given for the same slope and block. Also, is it really said that the string pulls horizontally to prevent the block from sliding? That is rather impossible.

It's NOT impossible. If the string acts to the left it will stop the block sliding down the slope.

If I've understood the problem it looks like this. There is a component of weight acting down the slope that must be balanced by the component of T acting up the slope.

If this is a multipart question and the first part gives you info on friction then you need to factor that in as well. Otherwise treat as frictionless.

#### Attachments

• Untitled.png
13 KB · Views: 1,125
Pranav-Arora said:
(see attachment)
The tension on the block acts as shown in the attachment, not in the x-direction. As i already said, a component of weight balances tension. Your job is to find that component.

Actually, the trick here is that the rope is actually perpindicular to the force of gravity.

CWatters said:
It's NOT impossible. If the string acts to the left it will stop the block sliding down the slope.

I just wonder how it can be realized. Imagine you tilt a table and put a book on it, you attach a string to the book, - how do you manage to pull the string horizontally? Drilling a hole through the table?

ehild

trolling said:
Actually, the trick here is that the rope is actually perpendicular to the force of gravity.

The weight of the block has a component parallel to the slope and an other component perpendicular to it. The horizontal force of tension also can be resolved into parallel and perpendicular components. The normal force balances the sum of both perpendicular components, those of the weight and the tension. Friction acts along the slope, upward.

ehild

## 1. What is the relationship between the angle of incline and the tension in the rope holding a block?

The tension in the rope holding a block on an incline is directly proportional to the angle of incline. This means that as the angle of incline increases, the tension in the rope also increases.

## 2. How does the weight of the block affect the tension in the rope on an incline?

The weight of the block has a direct effect on the tension in the rope. As the weight of the block increases, the tension in the rope also increases. This is because the weight of the block creates a downward force that the rope must counteract in order to keep the block in place on the incline.

## 3. What role does friction play in the tension of the rope on an incline?

Friction between the block and the incline can affect the tension in the rope. If there is a high amount of friction, the tension in the rope will need to be greater in order to keep the block in place. However, if there is little friction, the tension in the rope may be lower.

## 4. How does the length of the rope affect the tension on an incline?

The length of the rope does not have a significant effect on the tension in a block held on an incline. As long as the rope is long enough to reach from the block to the top of the incline, the tension will remain relatively constant. However, if the rope is too short, it may not be able to hold the block in place.

## 5. What happens to the tension in the rope if the angle of incline is changed?

If the angle of incline is changed, the tension in the rope will also change. As the angle increases, the tension will increase, and as the angle decreases, the tension will decrease. This is due to the change in the force of gravity acting on the block.