Mechanical energy of frictionless pulley

In summary, the problem involves a system with a block of mass 15.65 kg initially moving to the left at a speed of 3.4 m/s. The block m has a mass of 8.26 kg and is acted on by a tension force and frictional forces with coefficients of μs=0.411 and μk=0.304. A diagram is provided for visual reference. The goal is to determine the final speed of the block M when m has fallen through a height of 2.47 meters. The equations used in the attempt at a solution are Ef - Ei = Kf - Ki + Uf - Ui = -fkd + ∑ W_otherforces, where K is the kinetic
  • #1
Deadnotsleeping
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Homework Statement


In the system shown, the block M (mass of 15.65 kg) is initially moving to the left with a speed of 3.4 m/s The mass of m is 8.26 kg and the coefficients of friction are μs=0.411 and μk=0.304. The string is massless and the pulley is massless and frictionless. How fast will M be traveling when m has fallen through a height h=2.47 meters?

diagram: http://is.byu.edu/courses/univ/694820121008/media/8_problem_blockmass.jpg

Homework Equations


Ef - Ei = Kf - Ki + Uf - Ui = -fkd + ∑ W_otherforces

K = 1/2mv^2
U=mgy

The Attempt at a Solution


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Since M does not have any change in potential energy, but it is acted on by a tension force, I got

Ef - Ei = 1/2mvf2 - 1/2mvi2 = -fkd + T
where fkd = μkMgd and T = (( μk+1)Mg)/(1+M/m)

I solve for vf but keep getting the wrong answer. The answer should be about 4.32 m/s
What am I doing wrong?
 
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  • #2
Hello DNS, welcome to PF :smile: !

I looks like you are adding an energy (fkd) to a force (T) That can't be !

It also looks like your change in kinetic energy doesn't depend on M, which is very strange.

Finally, your energy balance should also have a term Uf - Ui which I miss in your solution attempt.

If you show your work, step by step, I may be able to answer your question. With the information you provide now it's impossible.

(And I do get 4.31 m/s if I use g = 9.81 m/s2 )
 

FAQ: Mechanical energy of frictionless pulley

What is mechanical energy?

Mechanical energy refers to the energy possessed by an object due to its motion or position. It is the sum of kinetic energy (energy of motion) and potential energy (energy of position).

What is a frictionless pulley?

A frictionless pulley is a pulley system that does not experience any friction or resistance when a force is applied. This allows for the conservation of mechanical energy as no energy is lost due to friction.

How is mechanical energy conserved in a frictionless pulley?

In a frictionless pulley, the tension in the rope on either side of the pulley is equal. This means that the amount of work done on one side of the pulley is equal to the amount of work done on the other side. Therefore, the mechanical energy of the system remains constant.

What is the equation for calculating mechanical energy in a frictionless pulley system?

The equation for calculating mechanical energy in a frictionless pulley system is: mechanical energy (ME) = potential energy (PE) + kinetic energy (KE). This means that ME = mgh + 1/2mv^2, where m is the mass of the object, g is the acceleration due to gravity, h is the height, and v is the velocity of the object.

Can mechanical energy be lost in a frictionless pulley system?

No, mechanical energy cannot be lost in a frictionless pulley system. This is because there is no friction or resistance, so no energy is converted into heat or sound. The mechanical energy of the system will remain constant as long as there are no external forces acting on it.

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