Why is Work Defined as Fd and not Ft?”

[boggleface]

Why is work defined as Fd? If you apply the same force to 2 different masses over the same distance surely the larger mass has more energy. Why isn't work defined as Ft??

 

[Adrian Baker]

If you apply the same force for the same time to two different masses (say a truck and a bicycle) you don't get the same result do you?

It takes more energy to move a truck 100m than it does a bicycle, so more work is done pushing it the same distance.

You also say "surely the larger mass has more energy" What do you mean by this? If I push a truck along a flat road, I do work moving the truck, but don't increase it's energy state.

 

[Adrian Baker]

Yes, I was considering friction.

My reply to the first post was started before you answered Ambitwistor, but posted AFTER yours went up. I was just giving a simple illustration of where boggleface had gone a bit wrong.
Your answer is a more complete one.


(Although actually, if you consider Friction, the truck tyres will have heated up a bit, so it WILL be in a higher energy state!)

 

[Chi Meson]

Originally posted by boggleface
Why is work defined as Fd? If you apply the same force to 2 different masses over the same distance surely the larger mass has more energy. Why isn't work defined as Ft??

Fd is work, which is equal to the change in kinetic energy (assuming there are no other forces on it at the same time)

Ft is impulse, which is equal to the change in momentum (same assumption)

The confusion between momentum and kinetic energy is common, especially since they are both quantities of mass in motion. The only way out of the confusion is to stick to the definitiona of each, until you "grasp" it mentally.

 

[boggleface]

No. What i mean is that Fd does not sit with my intuition about energy. I imagine 2 different masses bieng accelerated over the same distance with the same constant force. My intuition tells me that surley the larger mass will have more energy. NOTHING TO DO WITH FRICTION! why isn't mv named energy?Is it just me, am i strange?

 

[Integral]

You will find that physics frequently requires you to drop preconcieved notions in order to grasp the realities of the universe. Do not worry about how you think it ougth to be, concentrate on learning how it is.

 

[boggleface]

yeah I've heard this said many times about intuition and reality but never with regard to this

 

[boggleface]

im arguing over my intuative concepts not words

 

[boggleface]

If I'm pushing two different masses over the same distance with the same constant force, imagining that no friction is present on the masses, i am pushing the larger mass for a greater amount of time. Surely i have used more calories pushing the greater mass.

 

[boggleface]

well if I am in space, pushing 2 different masses with the same canstant force over the same distance, surley i feel that i have exerted myself more pushing the larger mass as i have applied the same force over a longer period of time to bring it to the same distance

 

[krab]

Originally posted by boggleface
well if I am in space, pushing 2 different masses with the same canstant force over the same distance, surley i feel that i have exerted myself more pushing the larger mass as i have applied the same force over a longer period of time to bring it to the same distance

"Exerted Myself" is not the same as "did Work", when work is defined as in physics. To make this clearer, let's try a different example. If you push something for a long period of time and it doesn't move, you feel as though you've expended energy. But with the physics definition, you've done no work. None. It may tire your muscles, you may have used up calories, but the work done on the object that did not move, and therefore its change in energy, is Zero. If you really want to account for the energy used by your body in the pushing, you can say that the efficiency of converting the food you ate into energy was Zero percent.

This is not just a thing about definitions. You are wrong if you think that it is force times time that matters in terms of bodily work done. Try pushing your wall with a 50 pound force for a minute. It's not "hard work". In fact you could rig up a stick to do the work for you, but that would be cheating. Now go out and push your car with a 50 lb force for a minute. Assuming the ground is level, it will start moving, and you'll have to maintain the same force in spite of doing it while walking/running. Check your pulse rate afterward. It will be much higher than when you pushed the stationary wall.

Other example: Take a multi-speed bicycle, and put it in a really tall gear. Apply as much force as you can to the pedals for one minute. Your muscles may cramp, but you won't be out of breath. Now choose the correct gear, apply the same amount of force for the same amount of time. By the end of this, you will be going much faster than in the tall gear case, and you will be way out of breath. These examples demonstrate that froce times time is not the relevant quantity to measure energy.

 

[zoobyshoe]

Since there is no friction once you get either mass into motion it will stay in motion until something other than friction stops it.

If the acceleration is the same, it will take a larger force to get the larger mass into motion than it will take to get the smaller mass into motion. If the acceleration is different the force will be different according to:

F=ma

 

[turin]

You burn calories for several reasons. The most relavent reason in this case is the energy required to cycle the states of the muscular fibers. For instance, you don't do physics work on a 100 lb. dumbell, by just holding it in your hand with your arm straight out from your body. However, this will certainly make you tired, and cause your muscles to fatigue. Even here, the fatigue is not even primarily caused by the lack of energy, but by a build-up of lactic acid. You will by the time you decide that you can't take any more and drop the dumbell, you have done precisely zero physics work on the dumbell, but, since your metabolism has presumably been functioning properly to keep your overall body alive, and since the muscle fibers have been expanding and contracting in your arm to hold the dumbell in place, you have used many Calories.