Kinetic Energy • associated with motion, velocity.• if v = 0, KE = 0.

Chap 5

Gravitational Potential Energy

mgyPEg

yi = 0

yf = h

• associated with position y.

• if y = 0, PEg = 0.

• you are free to choose where to assign y = 0. Normally y = 0 at the ground level. Independent of your choice of where y = 0 is, the change in PE will always have the same value (ΔPE is independent of where y = 0 is).

Gravitational Potential EnergyReference levels

Spring Potential Energy

2

2

1kxPEs

• associated with displacement of spring x.

• when x = 0, PEs = 0.

• x =0 is the position of equilibrium of the spring, and right there PEs = 0. Anywhere else, PE ≠ 0.

k is the spring constant, measured in N/m.

For flexible springs, k is about 100 N/m, for stiff springs it can be about 10000 N/m.

cos xFW

WORK• Not the same meaning as in everyday usage.• F and d must be parallel or antiparallel, otherwise work W = 0.• always think of work as ENERGY BEING TRANSFERRED.

A force of 50 N is used to drag a crate 4 m across a floor. The force is directed at an angle upward from the crate as shown. What is the work done by the horizontal

component of the force?a) 120 Jb) 160 Jc) 200 Jd) 280 Je) 0 J

The horizontal component of force is 40 N and is in the direction of motion: W = F · d

= (40 N) · (4 m) = 160 J.

What is the work done by the vertical component of the force?

a) 120 Jb) 160 Jc) 200 Jd) 280 Je) 0 J

The vertical component of force is 30 N but isn’t in the direction of motion: W = F · d

= (30 N) · (0 m) = 0 J.

What is the total work done by the 50-N force?

a) 120 Jb) 160 Jc) 200 Jd) 280 Je) 0 J

Only the component of force in the direction of motion does work: W = F · d

= (40 N) · (4 m) = 160 J.

Sometimes work is zero:watch out for the cosine!

• Displacement is horizontal

• Force is vertical• cos 90° = 0

Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal as in the figure below. {image}  Note: click here to see an animation that illustrates this situation.Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest.

In the figure below, a block moves to the right in the positive x-direction through the displacement while under the influence of a force with the same magnitude . Which of the following is the correct order of the amount of work done by the force , from the most positive to the most negative?

1. d, c, a, b

2. c, a, b, d

3. c, a, d, b

Quick Quiz 5.1

KE+

PE+W -W

TME

Internal work

Internal work

Work done by external forces

W W

Work done by external forces

=

TME = PE + KE

CONSERVATION OF ENERGY

BEFORE = AFTER

Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal as in the figure below. {image}  Note: click here to see an animation that illustrates this situation.Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest.

Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal as in the figure below. Neglect air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest.

1. 1, 2, 3

2. 2, 1, 3

3. 3, 1, 2

4. all three balls strike the ground at the same speed

Quick Quiz 5.2

Bob, of mass m, drops from a tree limb at the same time that Esther, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they reach the ground?

1. Bob's kinetic energy is greater than Esther's.

2. Esther’s kinetic energy is greater than Bob's.

3. They have the same kinetic energy.

4. The answer depends on the shape of the slide.

Quick Quiz 5.3

Types of Forces

• There are two general kinds of forces– Conservative

• Work and energy associated with the force can be recovered

– Nonconservative• The forces are generally dissipative and work done

against it cannot easily be recovered

Conservative forces are forces for which the energy can be completely recovered.

– Gravity and elastic forces are conservative.– Friction is not conservative.

Energy Transformation for a Pendulum

Energy Transformation on a Roller Coaster

If W = 0, then TME = KE+PE = constant

Non-conservative forces:Friction Depends on the Path

• The blue path is shorter than the red path

• The work required is less on the blue path than on the red path

• Friction depends on the path and so is a non-conservative force

KE+

PE+W -W

TME = KE + PE ± Wext

Internal work

Internal work

Work done by external forces

W W

Work done by external forces

our system

isgfsgnc PEPEKEPEPEKEW )()(

If nonconservative forces do work, then the equation for

CONSERVATION OF ENERGY changes:

DISSIPATIVE forces acting on Downhill Skiing

If W = 0, then TME = KE+PE = cte.

But in this case W ≠ 0, so TME will change.

Springs obey Hooke’s Law

A book of mass m is projected with a speed v across a horizontal surface. The book slides until it stops due to the friction force between the book and the surface. The surface is now tilted 30°, and the book is projected up the surface with the same initial speed v. When the book has come to rest, how does the decrease in mechanical energy of the book-Earth system compare to that when the book slid over the horizontal surface?

1. It's the same.

2. It’s larger on the tilted surface.

3. It’s smaller on the tilted surface.

4. More information is needed.

Quick Quiz 5.4