Energy conservation and friction

[otownsend]

Hi,

I just started learning physics at university and so I'm looking for help on a simple energy conservation problem. On the bottom right-hand of the image I attached below, you should see that it asks whether the initial speed would increase or decrease if the object was of a greater mass... why would the speed not change? In the calculations for initial speed, the co-efficient of static friction is included which varies depending on what surfaces are in contact with each other. I would therefore believe that the initial speed of the larger mass object would be greater, since the co-efficient would also be greater. Can someone please clarify this for me?

 

[DrClaude]

Hi,

I just started learning physics at university and so I'm looking for help on a simple energy conservation problem. On the bottom right-hand of the image I attached below, you should see that it asks whether the initial speed would increase or decrease if the object was of a greater mass... why would the speed not change? In the calculations for initial speed, the co-efficient of static friction is included which varies depending on what surfaces are in contact with each other. I would therefore believe that the initial speed of the larger mass object would be greater, since the co-efficient would also be greater. Can someone please clarify this for me?

Look at the equation just above "Solve and evaluate." You will notice that the mass enters on both sides of the equation. So yes, the friction will be greater with the greater mass of the vehicle, but so will its kinetic energy. The two cancel out and the result is independent of the mass of the object.

 

[otownsend]

Look at the equation just above "Solve and evaluate." You will notice that the mass enters on both sides of the equation. So yes, the friction will be greater with the greater mass of the vehicle, but so will its kinetic energy. The two cancel out and the result is independent of the mass of the object.

Oh I think I understand what you mean!

The co-efficient of kinetic friction is just determined by the contacting surfaces (rubber and concrete in this example) and so the mass of the object does not affect this value.

I believe I was under the impression that the co-efficient of kinetic friction was determined by the normal force of the object (which indirectly means the mass of the object), which actually is not the case. The coefficient is merely the relationship between contacting surfaces of the same type and is discovered when comparing the ratio between the normal force and the friction force ... right?

 

[A.T.]

The coefficient is merely the relationship between contacting surfaces of the same type...

They don't have to be of the same type.

... and is discovered when comparing the ratio between the normal force and the friction force ... right?

It's not "discovered when comparing the ratio", it simply is the ratio.

 

[Mister T]

The coefficient [...] is the ratio between the normal force and the friction force ... right?

Yes, but note that the ratio may or may not depend on the normal force. The usual approach is to adopt the approximation that the ratio is independent of the normal force and also independent of the speed.