Work Done By Friction on a Circular Ramp

But thank you for confirming that I'm on the right track!In summary, the work done by friction on the block from the top to the bottom of the rough quarter-circle ramp is -(1/2)mv^2 + mgR, where m is the mass of the block, g is the acceleration due to gravity, v is the speed of the block at the bottom, and R is the radius of the ramp. This is derived by equating the work done by gravitational potential energy and kinetic energy at the bottom.
  • #1
MyNewPony
31
0

Homework Statement



A small block of mass m is held at the top of a rough quarter-circle ramp of radius R as shown in the figure, and then released from rest. When it reaches the bottom of the ramp, it is moving with speed V. How much work did friction do on the block from the top to the bottom? Express your answer in terms of m, g, V and R.

th_WorkDonebyFriction.jpg


Homework Equations



W (nc) = [tex]\Delta[/tex]K + [tex]\Delta[/tex]U

The Attempt at a Solution



Work done by gravitational potential energy is equal to mgR. It turns into kinetic energy at the bottom. Therefore,

W = ((1/2)mv^2 - 0) + (0 - mgR)
W = (1/2)mv^2 - mgR

And since this the work done by the object, the work done by friction would be the negative value. Thus,

W = -(1/2)mv^2 + mgR

Am I on the right track?
 
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  • #2
Yes, that's actually the right answer. Why did you doubt that it was?
 
  • #3
ideasrule said:
Yes, that's actually the right answer. Why did you doubt that it was?

Haha, I'm not sure. I was never really good at deriving equations.
 

1. What is work done by friction on a circular ramp?

The work done by friction on a circular ramp is the energy expended to overcome the resistance of friction between a moving object and the surface of the ramp.

2. How is work done by friction calculated on a circular ramp?

The work done by friction on a circular ramp can be calculated using the formula W = Ff * d, where W is the work done, Ff is the force of friction, and d is the distance over which the object moves.

3. What factors affect the amount of work done by friction on a circular ramp?

The amount of work done by friction on a circular ramp is affected by the mass of the moving object, the angle of the ramp, and the coefficient of friction between the object and the surface of the ramp.

4. How does the work done by friction on a circular ramp affect the speed of the moving object?

The work done by friction on a circular ramp acts in the opposite direction of the motion of the object, so it slows down the object and reduces its speed.

5. Can the work done by friction on a circular ramp be positive?

Yes, the work done by friction on a circular ramp can be positive if the force of friction is in the same direction as the motion of the object. This can happen, for example, if the ramp is on an incline and the object is moving upwards.

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