Does Normal force ever do work?

[nindra]

I encountered a question on my TPR Physics diagnostic test. It says that Normal force cannot change the speed of an object that's moving along a surface. Normal force, however, when acting as centripetal force, can change the object's velocity, but there is no work done because acceleration is perpendicular to the velocity.

Is there any case in which Normal force does work (something that's relevant to MCAT discussion)?

Thanks

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[chiddler]

Don't think so. normal force is just the force that opposes weight when on a surface so that the object does not fall inside the floor.

or, as my friend just put it, "does normal force cause it to go any distance?"

 

[howlovely]

I don't think so.

Like TPR said, the normal force is always applied perpendicular to an object by the surface of another object. Forces that do work must be applied in a direction parallel to the object's displacement. (In cases where a force is applied at an angle, only the component of the force that is parallel to the object's displacement does work.)

Say you have a box sitting on a table. The normal force that the table applies to the box is pointing up. In order for the normal force to do work, the box must be moved in an upward direction, but as soon as the box loses contact with the table, there is no more normal force.

 

[DrRichand1]

The only time i've seen it come up it when friction is involved where you need the normal force to find the work done by friction. It is not a direct force but effects work indirectly

 

[red doctober]

Normal force can actually do work. Just keep in mind that for any force to do work, there must be a component of the force that is in the direction of the displacement.

An example could be someone jumping up. The person experiences a displacement, and the normal force of the ground on the person does work on the person.

Another example could be a mass on an inclined plane. There's only two forces at work here (if ignoring friction): gravity and normal force. Now, gravity does work in the y-dimension, but the normal force is what does the work in the x-dimension.

 

[howlovely]

I've never thought of the jumping situation before, that's really interesting!

However, when a mass is on an inclined plane (ramp), only gravity does work when you assume that there's no friction. The force of gravity points straight down no matter what, while the normal force points perpendicular to the surface of the inclined plane. In this case, it's easiest to reorient the axes so that the x-axis lies on the same line as the inclined plane. The normal force "cancels" the y-component of gravity, which is mg*cos(theta) in this situation. The x-component of gravity, mg*sin(theta), is the only force that does work.

 

[red doctober]

I've never thought of the jumping situation before, that's really interesting!

However, when a mass is on an inclined plane (ramp), only gravity does work when you assume that there's no friction. The force of gravity points straight down no matter what, while the normal force points perpendicular to the surface of the inclined plane. In this case, it's easiest to reorient the axes so that the x-axis lies on the same line as the inclined plane. The normal force "cancels" the y-component of gravity, which is mg*cos(theta) in this situation. The x-component of gravity, mg*sin(theta), is the only force that does work.

Ah, how correct you are. Another situation I thought of is if the surface on which a mass is placed is being raised (like a table that a block is sitting on.) Whatever is raising the table is doing work on the table, but the normal force that the table exerts on the mass does positive work on the mass.

 

[Tatiana3325]

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An example could be someone jumping up. The person experiences a displacement, and the normal force of the ground on the person does work on the person.

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Actually, no, because in this example the ground does not move therefore there is no displacement and no work is done on the jumping person.

 

[red doctober]

Actually, no, because in this example the ground does not move therefore there is no displacement and no work is done on the jumping person.

If you're right, you're gonna have to tell me what else is doing work on the person then.

Here's how I think of this situation. There are 2 time points of interest here: 1) the person has his knees bent and is about to straighten them into a jump and 2) the person has straight legs and his feet are just about to leave the ground. Assume that the person's center of mass at time point 1) is lower than at time point 2). If there was no normal force (as if he were floating in space), the person would simply extend his legs and wouldn't accelerate in any direction. Thus, the normal force is required to move the center of mass vertically. The displacement that is needed for the work equation W=int(f*dx) is the displacement of the center of mass from 1) to 2). The normal force won't be constant through this process; it will decrease to zero at point 2). At point 2) the work is equivalent to the persons KE.

I'm not a physics guru and am not 100% positive that I am correct here, but I have always thought this is a valid situation where normal force can do work.

 

[Arctangent]

I would imagine that this occurs in an elevator to an object resting on the floor of the elevator. For a person standing in an elevator, the floor is what directly exerts a force on the person. Given nonzero vertical motion, and a nonzero normal force on the person (only when the elevator and thus the person inside are in free fall), there would be work done.

 

[Tatiana3325]

If you're right, you're gonna have to tell me what else is doing work on the person then.

Here's how I think of this situation. There are 2 time points of interest here: 1) the person has his knees bent and is about to straighten them into a jump and 2) the person has straight legs and his feet are just about to leave the ground. Assume that the person's center of mass at time point 1) is lower than at time point 2). If there was no normal force (as if he were floating in space), the person would simply extend his legs and wouldn't accelerate in any direction. Thus, the normal force is required to move the center of mass vertically. The displacement that is needed for the work equation W=int(f*dx) is the displacement of the center of mass from 1) to 2). The normal force won't be constant through this process; it will decrease to zero at point 2). At point 2) the work is equivalent to the persons KE.

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We are specifically discussing whether or not normal force is doing work on a person who jumps from a standing position. The answer is no. For work to be done there must be displacement in the direction of the applied force. The person is applying force to the ground. The ground does not move. No work has been done. The point of normal force is that it cancels out the force of gravity so that no acceleration is taking place in the Y direction.

If you ran arms out at a cement wall, you'd hit it and fall backwards. In that case you applied force to the wall, there was no displacement and therefore no work was done. You could spend all day stomping on the ground applying force. Still, no work done unless the ground moves in the direction of the applied force.