# Energy conversions

A car is made to decelerate down a slope. The force applied by brakes does a work of 350kJ. The change is kinetic energy is 270kJ. Why are these two values not equal to each other? I don't get what this means . The marking scheme says that the difference is loss in potential energy. I mean what does Ep have to do with anything?

• imagine the car is on a really steep slope. the brakes would do a lot of work but barely slow the car down – pentane Apr 28 '18 at 22:29

Work done by the breaks is sucking out energy and converting it into heat from not only the initial kinetic energy but also the initial potential energy.

Initially, at the high starting point, the car has kinetic energy. Now, potential energy is also stored due to the height. If the car fell freely with no brakes or friction (no work being done), then potential energy is converted into kinetic energy during the fall.

If something such as brakes is slowing it down, then it must absorb both the initial kinetic energy as well as the generated kinetic energy, which equals the loss in potential energy exactly.

Therefor the work done (corresponding to energy absorbed) is not equal to the initial kinetic energy, but does depend on the initial potential energy.

• Thank you! So does work done by brakes always mean that energy is lost in form of heat? Could please explain what does work done by something mean? For example what does positive work done by gravity mean? Does it mean loss in potential energy? – Seerat Fatima Apr 28 '18 at 23:56
• @SeeratFatima If it is brake clamps pushing on a disc and slowing you down through friction, then yes, the energy is converted into heat and lost. But you could also imagine eg a spring being wound up while slowing down the wheels. Then the energy would be converted into elastic potential energy and would not be lost, but stores inside the spring. Friction brakes are just way more common. – Steeven Apr 29 '18 at 7:01
• @SeeratFatima "what does work done by something mean?" There are two means of energy transfer in this world: thermodynamic and mechanic. We call them heat and work. Energy is transfered as heat when thermal energy is provided (or taken away), while energy is transfered as work when mechanical displacement is done (or prevented) by a force. So every time a force causes something to move (or slows something down) then that is work being done. Gravity pulling in the Apple thus only does work on it, when the Apple actually falls. – Steeven Apr 29 '18 at 7:05
• @SeeratFatima "For example what does positive work done by gravity mean? Does it mean loss in potential energy?" As mentioned, if gravity moves something (or slows it down), then it does work. If that work energy is added to the object/system, then we call it positive. Else více versa. Now, since gravity is a conservative force, then the work that gravity can do is called gravitational potential energy. – Steeven Apr 29 '18 at 7:08

Well, if it's a slope, there's two energies involved: kinetic and gravitational potential energy.

Let's call Kinetic Energy: T , and Gravitational energy: U

The TOTAL loss of energy (that which the brakes did) is 350kJ, however, you only lost 270kJ of that in the form of Kinetic energy, therefore, the other 80kJ were lost in gravitational potential energy.

That's the math, but... It actually makes physical sense! If the car is going DOWN the slope, we are losing height (considering that our gravity acts towards the "ground")

If I remember correctly, the simplest formula for it goes like dU = mgdh where the "d"s are variations of the corresponding variable. (m being mass and g being the gravitational constant for events taking place way below the limit of the troposphere and h being a height)

So, as the car goes down, the brakes have to act agaisnt both the energy from the body's height and it's speed! Thus we have 80kJ depleted from the Gravitational energy!