# Does more energy equate to more force?

1. Feb 18, 2012

### sgstudent

Since energy is changed to work done, and the distance will be constant, the only variable is the force. So 100N compared to 50N will have double the force. So does it mean more energy more force?

Thanks for the help!

2. Feb 18, 2012

### tiny-tim

hi sgstudent!

energy doesn't cause force

for example, if we drop something then yes it gets more energy, but that's because a force (gravity) is working on it

what situation did you have in mind?​

3. Feb 18, 2012

### sgstudent

Something like, when I whack a hammer onto a nail. With more energy I whack the hammer will there be more force?

Since kinetic energy changes to work done, so work done equal force x distance. Since distance is greater, then there will be more force? Then again if the hammer hits with constant velocity then the hammer will have no energy, but when it 'imparts' that energy to the hammer then work done occurs?

4. Feb 18, 2012

### tiny-tim

i don't know why you're calling that "energy"

your arm is using force to move the hammer, not energy

and the hammer is being supplied with momentum rather than energy …

it's the change in the hammer's momentum (when it is stopped by the nail) that gives momentum to the nail

5. Feb 18, 2012

### sgstudent

Sorry I'm taking O levels so I have not learnt momentum yet. What I'm trying to say is: when I whack using a hammer into a nail, I have a certain amount of kinetic energy using the formula 1/2mv^2 then that energy is converted to work done to push the nail in. So with a greater kinetic energy there will be s greater work done right? And since the nail will move in the same distance, the force will be more when energy is more.

Is this right too? Thanks for the help!

6. Feb 18, 2012

### tiny-tim

that's what was puzzling me …

why will the nail move the same distance?

surely if you hit it harder, it wil go in further?

7. Feb 18, 2012

### juanrga

ΔE = W = - FΔX

Yes double energy (ΔE → 2ΔE) means double work (W → 2W) and if distance is constant double force (F → 2F) being applied.

8. Feb 18, 2012

### sgstudent

Oh but if the nail doesn't go in as much then what would happen?Im really confused about the two concepts I understand what force is but I don't know the relationship between the them...
Could u explain this to me?

Thanks for the help!:)

9. Feb 19, 2012

### Staff: Mentor

Perhaps I can help clear up some misunderstandings. The hammer HAS energy and momentum when you are swinging it and are about to hit the nail. Energy is just a measure of the ability to do work. Upon impact the hammer exerts a force against the nail, and it is this force that pushes the nail in, not work or energy. However, the nail also pushes back equally, which is what causes the hammer to stop when it hits the nail.

Now, just because a hammer has more energy doesn't mean it has a higher force. If you hit the nail with a hammer, and then put it down and pick up another hammer which has twice the mass and swing it at the same speed it will still exert the same force as the first hammer. However, the 2nd hammer has twice momentum and energy as the 1st one and it will take more work (and energy) to swing it AND to stop it. Put simply, momentum is a measure of how hard it is to stop an object and is a product of the object mass times it's velocity, or p = mv. This means that it will take longer to slow down after it hits the nail, causing the nail to get hammered in further than with the first hammer.

But we can also get twice the momentum with the 1st hammer by swinging it twice as fast. HOWEVER, as Ke = 1/2mv^2 tells us, it takes 4 times as much energy to swing the hammer twice as fast. So to hit the nail in further we can either use a heavier hammer or swing the same hammer faster. The reason we don't walk around with huge hammers everywhere just tapping nails in is because it takes a lot of energy and effort to carry big hammers around compared to small hammers!

(I THINK that's all pretty much correct. Someone let me know if I've butchered physics somewhere)