Friction and normal force on an incline

In summary, the conversation discusses two slopes, A and B, with different inclines but the same vertical height. Using the work energy theorem, it is determined that the work done against friction and initial kinetic energy are equal to the gain in gravitational potential energy in both slopes. However, it is also noted that the distance covered by a body sliding down slope A is less than slope B, resulting in a larger work done against friction in B. This leads to the conclusion that the body in A will have more kinetic energy at the end of the slope. The conversation also addresses the difference in normal force between the two slopes due to the different angles of inclination. Ultimately, the importance of specifying all conditions in a problem is emphasized.
  • #1
sgstudent
739
3
I have an incline A that is very steep reaching a vertical height of h and another one B which is less steep with the same vertical height. So using the work energy theorem: in A, KE+work done against friction=mgh so the work done against friction and initial KE is equal to the gain in gravitational potential energy. In B, KE+work done against friction=mgh also. So again the work done against friction and intial KE is equal to the increase in mgh.

So from this we can say that the work done against friction is equal to each other as in both cases the initial KE is the same as each other. (KE+work done=KE+work done). But in A, the distance is lesser than in B. Since work done=forceXdistance so the friction in A is greater than in B?

And since friction is the coefficient of friction multiplied by the upwards force, since the roughness is assumed to be the same for this example, as A is greater than B and the coefficient is the same so won't A have a greater normal upwards force? Thanks for the help :smile:

image:http://postimage.org/image/590thw81f/full/
 
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  • #2
You are contradicting yourself. As you have assumed, the frictional force is the same in both cases. As a result, the work done in B would be more than the work done in A because the distance covered by a 'body' sliding down slope A would be less than B, hence, less work is done against friction in A as compared to B.

By Principle of Conservation of Energy, the final total energy must be equal to the initial total energy. Given that in both cases, the 'body' possesses the same amount of initial Gravitational Potential Energy, the final total energy must be the same. As a result of larger work done against friction in B, the 'body' in A will possesses more Kinetic Energy at the end of the slope.Now, visiting the question about the Normal Force, you can draw out the free-body diagram to see it for yourself. The resultant force of Friction and Normal force should be opposite and of the same magnitude with Weight. What you get would be a larger Normal force in case B.

Hope that helps :)
 
  • #3
Nguyen Quang said:
You are contradicting yourself. As you have assumed, the frictional force is the same in both cases. As a result, the work done in B would be more than the work done in A because the distance covered by a 'body' sliding down slope A would be less than B, hence, less work is done against friction in A as compared to B.

By Principle of Conservation of Energy, the final total energy must be equal to the initial total energy. Given that in both cases, the 'body' possesses the same amount of initial Gravitational Potential Energy, the final total energy must be the same. As a result of larger work done against friction in B, the 'body' in A will possesses more Kinetic Energy at the end of the slope.Now, visiting the question about the Normal Force, you can draw out the free-body diagram to see it for yourself. The resultant force of Friction and Normal force should be opposite and of the same magnitude with Weight. What you get would be a larger Normal force in case B.

Hope that helps :)

I'm not sure what you mean because in http://www.physicsclassroom.com/mmedia/energy/au.cfm it shows that the work done to bring it up is the same. So KE+work done against =mgh for both cases right?

I didnt say that the friction was the same. I mentioned that the work done against friction is the same. Again you contradict yourself with the normal force. In both examples the normal force is different due to the different angles of inclination as I mentioned in the start. Since friction is μN and N is different the friction cannot be the same?

Is there something wrong with my theory here? Thanks for the help :smile:

Hi I also edited the first post to make it clearer.
 
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  • #4
I agree with you on the part where KE+work done against =mgh. I did not disagree with it. It adheres to the principle of Conservation of Energy.

I will get this straight. The Normal force and friction force are different in both cases. The work done against friction is also different in both case.

The real problem is that your question does not specify any details on the slope as well as the 'body' in motion. As such, I have to assume one variable to be constant to tell you the exact answer. If you want to consider both variables then there will be no exact answer.
 
  • #5
If they both start with the same KE, they will not reach the same height, h, due to the friction.
So you have either the same KE and different values of h or same values of h but different initial KEs.
It would be useful for both yourself and people reading your posts, to specify the actual problem, with all conditions. Playing with equations out of context is quite useless and confusing.
 
  • #6
sgstudent said:
in A, KE+work done against friction=mgh
It's not clear which way the block moves. If it starts at the top at rest and slides down then yes, final KE+ work against friction = mgh. But it sounds like it starts at the bottom with some initial KE and comes to rest at the top. In this case friction moves to the other side: initial KE = mgh + work against friction.
so the work done against friction and initial KE is equal to the gain in gravitational potential energy. In B, KE+work done against friction=mgh also. So again the work done against friction and intial KE is equal to the increase in mgh.

So from this we can say that the work done against friction is equal to each other as in both cases the initial KE is the same as each other.
It depends what's the same and what's different in the two set-ups.
If the coefficient of friction is the same and the height is the same, the work done against friction cannot be the same. The normal force varies as cos(θ) (angle of slope to horizontal), so the dynamic friction does too. The distance the force moves, for fixed h, varies as cosec(θ). So the work done must vary as cot(θ). It follows that the change in KE must be different.
 

1. What is friction and normal force on an incline?

Friction and normal force on an incline are two forces that act on an object when it is placed on an inclined surface. Friction is the force that opposes the motion of the object and normal force is the force that acts perpendicular to the surface of contact between the object and the incline.

2. How does the angle of incline affect friction and normal force?

The angle of incline affects both friction and normal force. As the angle of incline increases, the normal force decreases and the friction force increases. This is because the component of the weight of the object acting perpendicular to the incline decreases, while the component acting parallel to the incline increases.

3. Which force is responsible for keeping an object from sliding down an incline?

The normal force is responsible for keeping an object from sliding down an incline. It is equal and opposite to the component of the weight of the object acting perpendicular to the incline, and balances out the force of gravity pulling the object downwards.

4. How does the coefficient of friction affect the friction force on an incline?

The coefficient of friction is a measure of the roughness between two surfaces in contact. A higher coefficient of friction means there is more resistance to motion and therefore a greater friction force. On an incline, a higher coefficient of friction would result in a greater friction force acting on the object.

5. Does the mass of the object affect the friction and normal force on an incline?

Yes, the mass of the object does affect the friction and normal force on an incline. The greater the mass of the object, the greater the normal force required to balance out the force of gravity. This in turn affects the friction force, as it is directly proportional to the normal force.

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