Conservation of Energy and Momentum

Central Concept: The laws of conservation of energy and momentum provide alternate approaches to predict and describe the movement of objects.

2.1 Interpret and provide examples that illustrate the law of conservation of energy.

Mechanical energy is categorized as potential energy and kinetic energy. Potential energy is stored energy and is created by doing work against a restoring force. When an object is moved against gravity or against a spring or against a rubber band, we say that it has stored energy because when it is released, the restoring force "automatically" pushes it back to where it was. I takes 1 Joule of energy to do 1 Newton-meter of work to store 1 Joule of potential energy. In Newtonian physics, energy always comes from other energy. So, we say that energy is conserved because its total never changes. In the real world, we sometimes say energy is "lost" when it becomes heat or sound or light and the amount of mechanical energy does go down, but the overall total of all energy should still be the same.

Example MCAS question for 2.1

2.2 Interpret and provide examples of how energy can be converted from gravitational potential energy to kinetic energy and vice versa.

Gravitational potential energy is energy stored by an object that is up at a height and can fall down. Because of gravity, it has a stored energy that causes it to move downward when it is released. As it moves downward, it loses potential energy and gains kinetic energy as it speeds up. Without friction, the kinetic energy the object has at the bottom is the same as the potential energy it had at the top. If something is fired into the air, the speed it has goes down as the kinetic energy is transferred to potential energy as it goes higher up. At the top it stops and has no kinetic energy and maximum potential energy before the energy is transferred back to kinetic energy as it falls down and speeds up.

Example MCAS question for 2.2

2.3 Describe both qualitatively and quantitatively how work can be expressed as a change in mechanical energy.

When something falls, both the potential and kinetic energies change. The amount they change is equal to the work done by gravity. If we know the force acting on an object and the distance it moves in the same direction as the force, then multiplying those two quantities gives work. If 10 Nm of work is done, it took 10 J of energy to do it and it could change the energy of an object by 10 J.
Because of friction in the real world, some mechanical energy is "lost" because it becomes heat or vibration energy. If we ignore that loss, the amount of work done and the amount of energy "used" and "gained" or "transferred" are all the same.

Example MCAS question for 2.3

2.4 Describe both qualitatively and quantitatively the concept of power as work done per unit time.

Power measures how fast work is done. So, if more work is done is the same amount of time or it takes less time to do the same amount of work, then the power is higher. We calculate power by taking the work done divided by the time it takes.

Example MCAS question for 2.4

2.5 Provide and interpret examples showing that linear momentum is the product of mass and velocity, and is always conserved (law of conservation of momentum). Calculate the momentum of an object.

When we multiply together mass and velocity we get momentum. Momentum is a combination of how much mass is moving and how fast its moving. A large object moving slowly or a small object moving fast might have the same momentum. When objects collide, the total momentum stays the same; it is conserved. If a moving object hits a stationary object, they will both move after the collision, but they will be moving slower than the original speed of the moving object.

Example MCAS question for 2.5