Which block dissipates the most mechanical energy by friction?

  • Thread starter StonieJ
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In summary, three identical blocks move in three different settings: block A on a horizontal surface, block B on an inclined plane, and block C down an inclined plane. They all start with the same speed and continue until brought to rest by friction. Based on the magnitude of the frictional force, the blocks dissipate energy in the following order, from least to greatest: block B, block A, block C. This may seem counterintuitive, but it is due to the fact that block B gains potential energy in exchange for kinetic energy while moving up the inclined plane.
  • #1
StonieJ
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Three identical blocks move in three different settings. Block A moves on a horizontal surface, block B moves up an inclined plane, and block C moves down an inclined plane. They all start with the same speed and continue until brought to rest by friction. Rank which block dissipates more mechanical energy by friction, least to greatest.



I am not very good with these "conceptual" questions, so I'm having a hard time even finding out where to start. I've been trying to calculate the forces of friction for each block (e.g. fA = u * mg, fB = u * mg * cos(T), etc) but it hasn't helped much. So, I was hoping somebody could at least give me a push in the right direction.
 
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  • #2
The frictional force is proportional to the normal force on the block.
In which situation is the normal force greatest?
 
  • #3
Well, your answer is encouraging because that's what I was doing originally, i.e. calculating the forces of friction on each block.

Block A
fA = u * mg
For block A, the normal is simply the mass times acceleration due to gravity.

Block B
fB = u * mg * cos(T)

Block C
fC = u * mg * cos(T)

For blocks B and C, the normal force is only a fraction of the mass times acceleration due to gravity.

So, based on that, I would say that block A dissipates energy the fastest and B and C dissipate energy equally. It's just that, intuitively, I have a hard time seeing this. Intuitively, I would be inclined to say that the block going uphill dissipates energy the fastest, followed by the block on the flat surface, followed by the block going down the plane.
 
  • #4
The block going uphill will probably come to a halt faster, but that doesn't mean it dissipates energy faster. It gains potential energy in return for kinetic energy. (it stops faster, but not due to friction).
You're asked for the dissipation in energy due to friction, so all you need is the magnitude of the frictional force.
I agree it's not very intuitive, but many things in classical mechanics aren't even though you'd expect otherwise.
 
  • #5
I think you can use kinetic energy and potential energy.
For block A the kinetic energy (1/2)mv^2= energy dissipated on friction(onA).
For block B the kinetic energy (1/2)mv^2= energy dissipated on friction(on B) +mgh' => (1/2)mv^2-mgh'= energy dissipated on friction(onB).
Finally, for block C (1/2)mv^2+mgh"= energy disspated on friction(onC).
kinetic energy is the same for the three cases because the have the same velocity and mgh'>0 and also mgh">0=>
energy dissipated on B< energy dissipated on A< energy dissipated on C.
 

What is friction?

Friction is a force that opposes the motion of an object. It occurs when two surfaces are in contact and trying to move against each other.

How is friction measured?

Friction is measured using a unit called the coefficient of friction, which is a number that represents the amount of force required to move an object over a surface.

How does friction affect work?

Friction can make it more difficult to do work, as it requires more force to move an object against its opposing force. Friction also causes energy to be lost as heat, which can impact the efficiency of work.

What is the relationship between friction and energy?

Friction converts some of the energy of motion into heat, which can be seen as a loss of energy. This can impact the performance of a system and the amount of work that can be done.

How can friction be reduced?

Friction can be reduced by using lubricants, such as oil or grease, between two surfaces. Another way to reduce friction is by smoothing or polishing the surfaces to make them smoother and reduce the amount of contact between them.

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