# Acceleration and tension of a block on an inclined plane

• Like Tony Stark
In summary, the conversation revolved around solving Newton's equations for ##m_1## and ##m_2## and determining the tension and acceleration in the system. There was a mistake in the equation for ##m_2## which was corrected to ##2T-W_{m_2}=0##. It was also advised to work algebraically and only substitute numbers at the end for easier understanding and checking of the reasoning.
Like Tony Stark
Homework Statement
The coefficient of static and dynamic friction are 0.45 and 0.3 respectively. Find the maximun value that ##m_2## could have so that the system is in equilibrium. Then, if ##m_2## is the double of the mass calculated previously, determine what's the acceleration of the system.
Relevant Equations
Newton's equations
I considered the downwards direction and left direction as negative. For ##m_1##, Newton's equations are:
##x) Fr + W_x - T=0##
##y) N - W_y =0##

For ##m_2##:
##y) T - W =0##

Then, if I replace the data, I get ##T=22.2 N## and then ##m_2=2.2 kg##.
With that, for the second question ##m_2=4.4 kg##, and then solving Newton's equations I get for ##m_1##
##x) 151.96 - T=20.a_x##
And for ##m_2## I get
##y) T -44=4,4a_y##.
Then ##a_x=a_y## and if I solve the system I get ##T=63.92 N## and ##a=4,39 m/s^2##

But I have some doubts with the sign of the acceleration and tension. The acceleration must be negative, because ##m_2## will be moving downwards and ##m_1## will be moving to the left.

#### Attachments

• 20190927_231233.jpg
44.9 KB · Views: 197
Like Tony Stark said:
For ##m_2##:
##y) T - W =0##
Did you draw an FBD for that?

haruspex said:
Did you draw an FBD for that?
Yes, but I didn't upload a photo because I thought that the equations were enough

Like Tony Stark said:
Yes, but I didn't upload a photo because I thought that the equations were enough
Well, the equation is wrong. Take another look at the diagram. Can you describe it or upload it?

haruspex said:
Well, the equation is wrong. Take another look at the diagram. Can you describe it or upload it?

#### Attachments

• 20190928_144712.jpg
43.8 KB · Views: 183
It's a pulley with a rope running around under it. You only show one straight length of rope.

haruspex said:
It's a pulley with a rope running around under it. You only show one straight length of rope.
Oh, I forgot the other tension acting on ##m_2##, didn't I? Well, apart from that my calculations are ok? Don't I have to change anything in the signs of the acceleration?

Like Tony Stark said:
Oh, I forgot the other tension acting on ##m_2##, didn't I? Well, apart from that my calculations are ok? Don't I have to change anything in the signs of the acceleration?
Yes, you have a sign error.

Please develop the habit of working entirely algebraically. Refrain from plugging in numbers until the end. Where the question supplies only a number (like 30 degrees) replace it with a symbol, like θ.
This has many advantages, one being that it is much easier for others to follow and check your reasoning.

Like Tony Stark
haruspex said:
Yes, you have a sign error.

Please develop the habit of working entirely algebraically. Refrain from plugging in numbers until the end. Where the question supplies only a number (like 30 degrees) replace it with a symbol, like θ.
This has many advantages, one being that it is much easier for others to follow and check your reasoning.

haruspex said:
Well, the equation is wrong. Take another look at the diagram. Can you describe it or upload it?
Is the correct equation ##2T-W_{m_2}=0##?

Delta2 said:
Is the correct equation ##2T-W_{m_2}=0##?
Yes.

## 1. What is acceleration on an inclined plane?

Acceleration on an inclined plane is the rate at which the velocity of an object changes as it moves up or down the slope of the plane. It is affected by the angle of the incline, as well as the mass and force of the object.

## 2. How is the acceleration calculated on an inclined plane?

The acceleration on an inclined plane can be calculated using the formula: a = g * sin(θ), where "a" is the acceleration, "g" is the acceleration due to gravity (9.8 m/s²), and "θ" is the angle of the incline.

## 3. What is the relationship between the angle of the incline and acceleration?

The steeper the angle of the incline, the greater the acceleration will be. This is because more of the force of gravity is acting in the direction of the incline, rather than perpendicular to it.

## 4. How does the mass of the object affect the acceleration on an inclined plane?

The mass of the object has a direct impact on the acceleration on an inclined plane. The greater the mass, the more force is required to move the object up the incline, resulting in a lower acceleration. Conversely, a lighter object will experience a higher acceleration.

## 5. What is tension in relation to a block on an inclined plane?

Tension is the force that is exerted on an object by a string, rope, or cable. In the case of a block on an inclined plane, the tension comes from the string that is attached to the block and pulling it up the incline. The amount of tension is dependent on the mass and acceleration of the object.

Replies
18
Views
587
Replies
5
Views
1K
Replies
44
Views
2K
Replies
4
Views
3K
Replies
15
Views
1K
Replies
1
Views
762
Replies
68
Views
10K
Replies
11
Views
1K
Replies
30
Views
2K
Replies
26
Views
3K