Momentum and Energy
Physical Science II
Impulse
Units: Newton x seconds [=] kg meters/second
Ft = ∆(mv) = m ∆v
This equation shows that impulse (F x t) = change in momentum. You can either change the time of the impact or the velocity. When you want the force of impact to be small, extend the time of impact.
Examples: safety net of acrobats, boxer “rolling with the punch”, truck hitting a haystack and not a solid wall
On the other hand, if you want the force of impact to be large, have a small time of impact
Example: karate expert breaking a stack of bricks
Changes in velocity will change the impulse due to the change in momentum. Example: A moving car bouncing off of a wall with only a slight reduction in speed has a greater impulse than a car than comes to a stop when hitting that wall.
Minimizing Impact Force: extend the time of the collision
Elastic and Inelastic Collisions
An Elastic collision is one in which there is no permanent deformation. Good examples of elastic collision is a billiard ball colliding with another or a mass cart bumping into another with a spring in between. In an elastic collision both energy and momentum are conserved.
An Inelastic collision is one in which the objects stick together. Good examples of inelastic collisions are a ball of putty hitting and sticking to another ball or two railroad cars colliding and coupling together. In an inelastic collision momentum is conserved, but energy is not.
Energy
Energy is difficult to define – it is a property of all matter just like inertia. It allows for work to be done. There are many forms. For now we will focus on energy that is due to the positions of the interacting bodies (potential) or their motion (kinetic).
Units - If work changes energy and is measured in Joules, then it makes sense that the Joule is the official energy unit. It is not a vector.
Kinetic Energy
Energy of motion is called kinetic energy.
Kinetic energy = 1⁄2 mass x velocity^2
Notice that KE is proportional to the square of the velocity!
Momentum is inertia in motion
Momentum = mass x velocity
Unit: kg meters/second
Momentum is changed by force. The amount of momentum change is also affected by how long the force acts. The product of force and time is called impulse.
Work Energy Theorem
Conservation of momentum
Whenever a physical quantity remains unchanged during a process, that quantity is said to be conserved. Momentum is such a quantity. This idea is especially useful in analyzing collisions.
Collisions can be elastic (objects hit and bounce off each other without deformation or generation of heat) or inelastic (objects hit and deform, generate heat, stick together or all of the above). Momentum is always conserved in all collisions.