Work, Energy and

PowerTEST: TUESDAY 11/13

Work

Example Problem #1

A box slides down an inclined plane that is at an angle of 37° to the

horizontal. The mass of the block, m, is 35kg, the coefficient of kinetic

friction between the block and the ramp, μk, is 0.3 and the length of the ramp, d, is 8m.

a) How much work is done by gravity?

b) How much work is done by the normal force?

c) How much work is done by friction?

d) What is the total work done?

Example Problem #1

A box slides down an inclined plane that is at an angle of 37° to the

horizontal. The mass of the block, m, is 35kg, the coefficient of kinetic

friction between the block and the ramp, μk, is 0.3 and the length of the ramp, d, is 8m.

a) How much work is done by gravity?

b) How much work is done by the normal force?

c) How much work is done by friction?

d) What is the total work done?

Example Problem #1

A box slides down an inclined plane that is at an angle of 37° to the

horizontal. The mass of the block, m, is 35kg, the coefficient of kinetic

friction between the block and the ramp, μk, is 0.3 and the length of the ramp, d, is 8m.

a) How much work is done by gravity?

b) How much work is done by the normal force?

c) How much work is done by friction?

d) What is the total work done?

Example Problem #1

A box slides down an inclined plane that is at an angle of 37° to the

horizontal. The mass of the block, m, is 35kg, the coefficient of kinetic

friction between the block and the ramp, μk, is 0.3 and the length of the ramp, d, is 8m.

a) How much work is done by gravity?

b) How much work is done by the normal force?

c) How much work is done by friction?

d) What is the total work done?

What if the force is

not constant?

Example Problem #2

What is the work done by a spring that pushes and

object out from x=-x2 to x=-x1 (where x2>x1)?

Example Problem #3

A force F(x) acts on a particle. The force is related to the

position of the particle by the formula F(x) = Cx3, where C

is a constant. Find the work done by this force on the

particle when the particle moves from x = 1.5m to x = 3m.

Graphical Analysis

Work is the area under the curve of F vs d graph.

Force might be constant or might be variable.

Work-Energy Theorem

Example Problem #4

A tennis ball, m=0.06kg, is hit straight upward with an initial

speed of 50m/s. How high would it go if air resistance were

negligible?

Types of Force

Conservative

Obeys conservation

of energy

Examples

Spring force

Gravity

Non-conservative

Energy is transferred into

non-mechanical forms

Examples

Friction

Air drag

Example Problem #5

A box is projected up a long ramp with an incline of 37° to

the horizontal with an initial speed of 10m/s. If the surface of

the ramp is very smooth (frictionless), how high up the ramp

will the box go? What distance along the ramp will it slide?

Example Problem #6

A crash test dummy, m=40kg, falls off of a 50m high cliff. On

the way down, the force of air resistance has an average

strength of 100N. Find the speed with which he crashes into

the ground.

Net Work done by conservative & non-

conservative forces is equal to the change in

kinetic energy

But work done by conservative forces is also

equal to the negative of the change in

potential energy

Example Problem #7

The force acting on an object is given by F(x) = a/x2, where

a is a constant. Determine the potential energy of the

object as a function of x.

Calculus!

Power is the rate that work

is done… and has a lot of

equations!