How do I calculate the loss of mechanical energy due to friction?

Question

There's no specific problem I need solved at this time, but is there like a formula I can use to find this value?

Answer 1

How about learning the physics...then you can derive your own formulae.

Conservation of energy is the physics. That states a system has total energy TE = KE + PE + WE; where KE is kinetic (mechanical) energy, PE is potential energy, and WE is work energy. And that total energy remains fixed (constant) because energy is neither created nor destroyed.

What happens is that the make up of TE changes from time to time, and place to place. That is, for example, TE = PE only when there is no kinetic energy and no work is being done. When a block of wood of mass m is h meters above the floor, for instance, TE = PE = mgh; where g is gravitational acceleration. In other words, all the total energy is potential energy in this case.

If we let the block slide down a ramp without friction considered, then TE = KE = 1/2 mv^2 just before impact with the floor at the foot of the ramp. In other words, all the total energy is kinetic (mechanical) energy in this case.

What's cool about the conservation of energy law, it that the two TE's are equal to each other. So we have TE = PE = mgh = 1/2 mv^2 = KE = TE. And they are equal to each other because all the PE was converted to KE when the block slid. If you use the equations above, you can solve for the velocity v just prior to impact: v = sqrt(2gh), which you may recognize as a special case for one of the SUVAT equations.

So what happens to KE when friction is included? Friction represents work done by the sliding block to overcome the friction force F = kN = kmg cos(theta); where k is the friction coefficient, N is the normal weight of the block, and theta is the ramp's incline.

As there is work done against the friction, we have WE = Fd = kNd = kmg cos(theta) d; where d is the distance the block slides along the ramp. h = d sin(theta); so d = h/sin(theta) from release point to the foot of the ramp when h and theta are given.

So, here's the conservation of TE with friction included. TE = PE = mgh = 1/2 mv^2 + kmgh cot(theta) = ke + WE = TE. Thus, ke (the kinetic energy when friction is included) = PE - WE = mgh (1 - k cot(theta)) < KE without friction. And this clearly shows that mechancial (kinetic) energy is degraded by friction. This means that ke/KE < 100% efficiency when there is friction.

So, using the conservation of energy, I showed how friction degrades efficiency. And I did it without memorizing a big equation. The big equation, that shows the efficiency degradation, was derived from knowing PE = mgh, KE = 1/2 mv^2, and WE = Fd and these are fundamental equations all physics students need to know.

Let's go back to TE = KE + PE + WE for a moment. This is just a conceptual equation to show the various kinds of energy that could make up a system's total energy. We saw that, due to physical conditions, some of these terms may be zero (like TE = PE or TE = KE with the other terms zero).

But we did not mention that one or more of each term may in fact be multiple terms. For example, suppose we have a human cannonball lying in the cannor ready to be fired. What's the total energy TE? Well, nothing's moving; so KE = 0. And no work is being done on or by the human cannonball; so WE = 0. That leaves us with TE = PE in concept.

But wait a minute...there is PE in the compressed spring that will launch the cannonball and there is PE in the fact that the human is h distance above ground level while lying inside the barrel. Thus we have TE = PE = PE(S) + PE(h); where PE(S) = k delX^2 which is the work done by the spring when decompressed from a delX compression. And PE = mgh; where m is the mass of the human cannonball and h is her height above the ground whill resting on the spring.

In other words, there are two PE's that can be converted into kinetic energy or work energy somewhere along the trajectory of the human cannonball. And there might be more than one friction to expend WE. For example, friction along the barrel and air friction (drag) during flight are distinct possibilities.

Bottom line...learn the physics, not the equations. If you learn the physics, the equations will take care of themselves.

Answer 2

Energy Lost To Friction

Answer 3

This Site Might Help You.

RE:
How do I calculate the loss of mechanical energy due to friction?
There's no specific problem I need solved at this time, but is there like a formula I can use to find this value?

Answer 4

Use a vegetable bean dip like hummus instead of ranch dressing or possibly a fatty cream-based dip.

Answer 5

Teach your kids your selected sport (or have them educate you on theirs).

Answer 6

Set your laptop alarm to ring hourly—stand way up for 1 to 5 minutes each time it goes off.

Answer 7

Calculate the frictional force.

Multiply by the distance moved.

Answer 8

When out with a restaurant, ask the server to keep the bread, snack mix or chips and salsa that will come before the meal. If you are hungry, you'll be tempted.

Answer 9

Don't confuse being thirsty with hunger. Drink a glass of water when you feel hungry to see if that's what you're really craving.

Answer 10

Hover just above your chair in a squat position for 15 seconds every hour.

Answer 11

Eating liquid-based foods such because natural smoothies and low-sodium soup can assist you cut back on calories still feel full.