Mechanical Energy Problem/non-conservative forces

In summary, a body of mass m begins on surface A and slides without friction to surface B. It then moves horizontally to surface C, 5 meters away from B, and stops. Using the equations Ei = Ef and W = F.d, the friction force F is determined to be 2mh in Newtons, where m is the mass in kg, h is the vertical distance, and g is the acceleration due to gravity. The approach used is valid, but it would have been better to use an unknown variable for the horizontal distance and not specify units in the problem.
  • #1
fuvest
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Homework Statement


A body of mass "m" is let go from on top of a surface A, where it slides down to B(without friction). From that point on, it displaces itself on an horizontal surface 5 meters away from B, where it stops at C.
Being "m" a mass in kg
"h" in meters and g = 10 m/s^2
The value, in Newtons, of the constant friction force F when the body dislocates itself is:

Homework Equations


Ei = Ef
W = F.d

The Attempt at a Solution


My attempt was to set the change in kinetic energy equal to the total work. So therefore:
1/2mv^2 - mgh(converted from gravitational potential energy) = Tf
at the very end, velocity will be zero because it stops so:
-mgh = Tf
replacing the work done by friction:
-mgh = -F.5
.'. F = (10mh)/5 = 2mh

Is this approach correct? Would you guys suggest another one? Is another possible?
Thanks
 
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  • #2
fuvest said:
Is this approach correct?
Looks fine. Not sure about some of the signs, but since you have not stated your sign convention they may be fine.

For what it's worth, it is very poor style to specify that a variable represents the numerical value of a physical quantity when expressed in certain units ("m being a mass in kg..."). It would have been better to statethe horizontal distance as another unknown, s say, and not mention units at all. The answer would then have been mgh/s.
 

FAQ: Mechanical Energy Problem/non-conservative forces

What is mechanical energy?

Mechanical energy is the sum of potential energy and kinetic energy in a system. It is the energy that is associated with the motion and position of an object.

What are some examples of non-conservative forces?

Some examples of non-conservative forces include friction, air resistance, and drag. These forces can convert mechanical energy into other forms of energy, such as heat or sound.

How do non-conservative forces affect mechanical energy?

Non-conservative forces decrease the total mechanical energy in a system by converting some of it into other forms of energy. This means that the amount of mechanical energy decreases over time as these forces act on the system.

Can mechanical energy be conserved in the presence of non-conservative forces?

No, mechanical energy cannot be conserved in the presence of non-conservative forces. This is because these forces convert some of the mechanical energy into other forms, resulting in a decrease in the total mechanical energy of the system.

How are mechanical energy problems solved?

Mechanical energy problems are typically solved using the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. This means that the initial mechanical energy of a system will be equal to the final mechanical energy, taking into account any changes due to non-conservative forces.

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