Conservation of Energy Forms of Energy Mechanical Energy

Conservation of Energy

Forms of Energy Mechanical Energy Thermal Energy Other forms include

Law of Conservation of Energy n What you put in is what you get out n Total energy is conserved

Practical Applications n n n Gasoline converts to energy which moves the car A battery converts stored chemical energy to electrical energy Dams convert the kinetic energy of falling water into electrical energy

Example : step 1

Example : step 2

Example : step 3

Example : last step

Conservation of Mechanical Energy m = mass v = velocity g = gravitational acceleration h = height Kinetic Energy Potential Energy Total Energy ILYA, did you know that even though it was a bumpy ride, our energy remained constant!

Conservation of Mechanical Energy n We denote the total mechanical energy by n Since n The total mechanical energy is conserved and remains the same at all times

A block projected up a incline n n Point A (initial state): Point B (final state):

Questions : Trucks with the noted masses moving at the noted speeds crash into barriers that bring them to rest with a constant force. Which truck compresses the barrier by the largest distance?

2 Types of Forces n Conservative forces ¡ ¡ n Work and energy associated with the force can be recovered Examples: Gravity, Spring Force, EM forces Nonconservative forces ¡ ¡ The forces are generally dissipative and work done against it cannot easily be recovered Examples: Kinetic friction, air drag forces, normal forces, tension forces, applied forces …

The work done by a conservative force is independent of the path, and depends only on the starting and ending points. Pick any starting and ending points. Closed path, W=0. A W 2 W 1 B A W 1 = WAB W 2 = WBA W 1 + W 2 = 0 W 1 + W 3 = 0 W 3 W 1 B So, all paths from B to A take the same amount of work.

Path doesn’t matter! Initial Final

Conservative Forces n A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points ¡ ¡ The work depends only upon the initial and final positions of the object Any conservative force can have a potential energy function associated with it Work done by gravity Work done by spring force

Ex n. 1: Block-Spring Collision n A block having a mass of 0. 8 kg is given an initial velocity v. A = 1. 2 m/s to the right and collides with a spring whose mass is negligible and whose force constant is k = 50 N/m as shown in figure. Assuming the surface to be frictionless, calculate the maximum compression of the spring after the collision.

Nonconservative Forces n A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. ¡ ¡ The work depends upon the movement path For a non-conservative force, potential energy can NOT be defined Work done by a nonconservative force It is generally dissipative. The dispersal of energy takes the form of heat or sound

Problem-Solving Strategy n Define the system to see if it includes non-conservative forces (especially friction, drag force …) Without non-conservative forces n With non-conservative forces n Select the location of zero potential energy n ¡ n Do not change this location while solving the problem Identify two points the object of interest moves between ¡ ¡ One point should be where information is given The other point should be where you want to find out something

Ex n 2: Block-Spring Collision n A block having a mass of 0. 8 kg is given an initial velocity v. A = 1. 2 m/s to the right and collides with a spring whose mass is negligible and whose force constant is k = 50 N/m as shown in figure. Suppose a constant force of kinetic friction acts between the block and the surface, with µk = 0. 5, what is the maximum compression xc in the spring.

Connected Blocks in Motion n Two blocks are connected by a light string that passes over a frictionless pulley. The block of mass m 1 lies on a horizontal surface and is connected to a spring of force constant k. The system is released from rest when the spring is unstretched. If the hanging block of mass m 2 falls a distance h before coming to rest, calculate the coefficient of kinetic friction between the block of mass m 1 and the surface.

Ex n. 3 : Block on wheel of death To stay on loop, the normal force, N, must be greater than zero.

h Mass must start higher than top of loop

Vfin h Vmax = Vfin = h = 5/2 R

Potential Energy vs. Force