Block on a slope, friction related

In summary, the conversation is about finding the mass of a hanging block that will overcome friction but not move the 300kg block on a slope of 20 degrees with a coefficient of friction of 0.75. The first attempt involves calculating the force acting down the slope and using it to find the mass, but the person realizes they did not properly take friction into account. The second attempt involves finding the force required to keep the block on the slope still, using the formula F = mgsin20 + umgcos20, and solving for the mass. The final result is 314kg.
  • #1
Revolt
7
0
A 300kg block is sitting on a slope of 20 degrees, the coeff of friction is 0.75, if the block is connected to a mass hanging vertically via a pulley, what is the mass of the hanging block such that it will overcome friction but not move the block

F = mgsin20 for the force acting down the slope
F = mgcos20 for the force acting perpendicular to the slope



Have attached a PDF of my attempt, but basically I found the force acting down the slope and then used this as the force in my next equation to calculate the mass,

Getting a result of 384kg, I now realize I haven't properly taken friction into account and I am unsure of how to do this.
 

Attachments

  • konica1wo120130116103807[1].pdf
    232.9 KB · Views: 282
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  • #2
In your attempt you've added the two vector components together as if they are scalar quantities ie 1006 + 2765 = 3771. I suggest you draw a free body force diagram for the 300kg block. Are we to assume it is on the point moving upwards?
 
  • #3
Indeed, got another solution ill upload in a minute
 
  • #4
For some reason the scanner isn't working, but basically i found the force required to in effect keep the block on the slope still, using

F = mgsin20 + umgcos20

and from this force i used m=F/g to get the mass of the block, 314kg... this seem right ?
 
  • #5
Could someone maybe run through this and tell me if they get a matching 314kg for the other block? thanks
 
  • #6
Have uploaded a new file with my method, anyone comment please?
 

Attachments

  • vvvvvvvv.pdf
    475 KB · Views: 329
  • #7
Revolt said:
Have uploaded a new file with my method, anyone comment please?
Well...you should draw all the forces and components acting on the block and also show clearly your reasoning. Otherwise your calculations are correct.:smile:
 
Last edited:

FAQ: Block on a slope, friction related

What is a block on a slope?

A block on a slope refers to a scenario in which a solid object, or block, is placed on an inclined surface or slope. This can be seen in everyday situations, such as a book sliding down a ramp or a car driving up a hill.

How does friction affect a block on a slope?

Friction plays a crucial role in the movement of a block on a slope. It is the force that resists the motion of the block and causes it to slow down or stop. The amount of friction depends on the roughness of the surfaces in contact and the weight of the block.

What is the relationship between the angle of the slope and friction?

The angle of the slope affects the amount of friction acting on the block. As the slope becomes steeper, the force of gravity acting on the block increases, resulting in a higher normal force and more friction. This means that a block on a steeper slope will experience more resistance to motion compared to a block on a gentler slope.

How does the weight of the block impact friction on a slope?

The weight or mass of the block also affects the amount of friction on a slope. The greater the weight of the block, the stronger the force of gravity acting on it, resulting in a higher normal force and more friction. This means that a heavier block will experience more resistance to motion compared to a lighter block on the same slope.

How can friction be reduced for a block on a slope?

To reduce friction for a block on a slope, one can try to make the surfaces smoother by using materials such as wax or oil. Another option is to decrease the weight of the block, which will decrease the force of gravity and therefore, the normal force and friction. Additionally, reducing the angle of the slope can also decrease the amount of friction acting on the block.

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