A Level Mechanics Friction

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EmRep13
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#1
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#1
Question outline:

- box on rough inclined plane
- box kept in equilibrium by string with tension TN, acting at an angle of 20 degrees to the plane, upwards.

The question is to find the range of values for T.

The solution bank states that TMin is when the particle is on the point of moving down the plane, and that limiting friction would be acting up the plane. I understand that friction acts to oppose motion but since the string's tension keeps the particle up, surely to be on the point of moving down, friction must be acting to oppose that?
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EmRep13
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mqb2766
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#3
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(Original post by EmRep13)
Question outline:

- box on rough inclined plane
- box kept in equilibrium by string with tension TN, acting at an angle of 20 degrees to the plane, upwards.

The question is to find the range of values for T.

The solution bank states that TMin is when the particle is on the point of moving down the plane, and that limiting friction would be acting up the plane. I understand that friction acts to oppose motion but since the string's tension keeps the particle up, surely to be on the point of moving down, friction must be acting to oppose that?
The minimum tension is when friction is acting in the same direction, i.e. up the ramp. The net force is zero (equilibrium) so
Tension + friction = weight
Or
Tension = weight - friction
(We've resolved everything to be along the plane)

The max tension. Is when you're trying to pull the weight up the plane, so friction acts down the plane, like weight:
Tension = weight + friction

Any tension between these values will mean the weight will not move. Outside these two values, the system will not be in equilibrium.
Last edited by mqb2766; 1 year ago
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davros
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#4
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#4
(Original post by EmRep13)
Question outline:

- box on rough inclined plane
- box kept in equilibrium by string with tension TN, acting at an angle of 20 degrees to the plane, upwards.

The question is to find the range of values for T.

The solution bank states that TMin is when the particle is on the point of moving down the plane, and that limiting friction would be acting up the plane. I understand that friction acts to oppose motion but since the string's tension keeps the particle up, surely to be on the point of moving down, friction must be acting to oppose that?
You seem to be saying the same thing twice - I can't see a contradiction here unless it's the way you've phrased it or I've misunderstood totally
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EmRep13
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#5
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(Original post by davros)
You seem to be saying the same thing twice - I can't see a contradiction here unless it's the way you've phrased it or I've misunderstood totally
I see how I phrased that badly, sorry! What I'm trying to say is that in the case of TMin where the particle is on the point of moving down the plane, surely since the tension is trying to pull it up, friction must be acting down, to oppose that, not up... ohhh I just read your answer again - so at the minimum tension, the weight is the "main" force almost pulling it down, so friction acts up. At the max tension, weight becomes the ""smaller" force, as the particle is being pulled up, so friction acts down to oppose the "main" force of tension.
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EmRep13
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#6
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#6
(Original post by mqb2766)
Any tension between these values will mean the weight will not move. Outside these two values, the system will not be in equilibrium.
But surely at the values that aren't the extreme highest or the extreme lowest in the range, the particle is no longer in limiting equilibrium?
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mqb2766
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#7
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#7
(Original post by EmRep13)
But surely at the values that aren't the extreme highest or the extreme lowest in the range, the particle is no longer in limiting equilibrium?
Those are the two extreme values. Friction will ensure there is no movement when the net force (excluding friction) is less than the limiting friction value. When the net force (excluding friction) is greater than limiting frictikn, movement occurs.
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EmRep13
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#8
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(Original post by EmRep13)
I see how I phrased that badly, sorry! What I'm trying to say is that in the case of TMin where the particle is on the point of moving down the plane, surely since the tension is trying to pull it up, friction must be acting down, to oppose that, not up... ohhh I just read your answer again - so at the minimum tension, the weight is the "main" force almost pulling it down, so friction acts up. At the max tension, weight becomes the ""smaller" force, as the particle is being pulled up, so friction acts down to oppose the "main" force of tension.
I'm not quite sure how to phrase this but how do you know that tension and weight have the relationship where the max tension is almost greater than friction + weight and the min tension + friction is almost smaller than weight? Like does the fact that the box is in equilibrium allow you to assume that the forces interact that way with the addition of friction? Like what's to stop the minimum tension itself being enough to bring the box out of equilibrium by being "stronger" than the weight?
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EmRep13
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#9
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#9
(Original post by mqb2766)
Those are the two extreme values. Friction will ensure there is no movement when the net force (excluding friction) is less than the limiting friction value. When the net force (excluding friction) is greater than limiting frictikn, movement occurs.
I don't understand?
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mqb2766
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#10
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#10
(Original post by EmRep13)
I'm not quite sure how to phrase this but how do you know that tension and weight have the relationship where the max tension is almost greater than friction + weight and the min tension + friction is almost smaller than weight? Like does the fact that the box is in equilibrium allow you to assume that the forces interact that way with the addition of friction? Like what's to stop the minimum tension itself being enough to bring the box out of equilibrium by being "stronger" than the weight?
The weight and the Tension sum (well subtract) to produce a net force. That is what determines whether there is movement by comparing it to the value of limiting friction.
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EmRep13
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#11
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#11
(Original post by mqb2766)
The weight and the Tension sum (well subtract) to produce a net force. That is what determines whether there is movement by comparing it to the value of limiting friction.
Ah - I see! Thank you!
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mqb2766
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#12
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(Original post by EmRep13)
Ah - I see! Thank you!
and the sign of the net force determines direction (opposing friction for equilibrium or movement)
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EmRep13
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#13
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#13
(Original post by mqb2766)
and the sign of the net force determines direction (opposing friction for equilibrium or movement)
I see - and you stick with the sign you assigned for each direction the whole way through. I understand! Thanks so much!
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