Chapter 5

Work and Energy

6-1 Work Done by a Constant ForceThe work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:

(6-1)

6-1 Work Done by a Constant Force

In the SI system, the units of work are joules:

For person walking at constant velocity:

•Force and displacement are orthogonal, therefore the person does no work on the grocery bag

•Is this true if the person begins to accelerate?

Example 6-1. A 50-kg crate is pulled along a floor. Fp=100N and Ffr=50N. A) Find the work done by each force acting on th crateB)Find the net work done on the crate when it is dragged 40m.

Wnet = Wg + Wn + Wpy + Wpx + Wfr

Mechanical Energy

Types of Mechanical Energy

•Kinetic Energy = ½ mv2

•Potential Energy (gravitational) = mgh

•Potential Energy (stored in springs) = ½ kx2

6-3 Kinetic Energy, and the Work-Energy Principle

Wnet = Fnetd

but Fnet = ma

Wnet = mad

v22 = v1

2 + 2ad

a = v22 - v1

2 2dWnet = m (v2

2 - v12)

2We define the kinetic energy:

6-3 Kinetic Energy, and the Work-Energy Principle

The work done on an object is equal to the change in the kinetic energy:

• If the net work is positive, the kinetic energy increases.

• If the net work is negative, the kinetic energy decreases.

(6-4)

Example: A 145g baseball is accelrated from rest to 25m/s.A) What is its KE when released?B) What is the work done on the ball?

Potential Energy

• Potential energy is associated with the position of the object within some system

• Gravitational Potential Energy is the energy associated with the position of an object to the Earth’s surface

6-4 Potential Energy

In raising a mass m to a height h, the work done by the external force is

We therefore define the gravitational potential energy:

(6-5a)

(6-6)

6-4 Potential Energy

Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy.

6-4 Potential Energy

The force required to compress or stretch a spring is:

where k is called the spring constant, and needs to be measured for each spring. k is measured in N/m.

(6-8)

Conservation of Energy

• Energy cannot be created or destroyed• In the absence of non-conservative forces

such as friction and air resistance:

Ei = Ef = constant

• E is the total mechanical energy

fsgisg )PEPEKE()PEPEKE(

Example: A marble having a mass of 0.15 kg rolls along the path shown below. A) Calculate the Potential Energy of the marble at A (v=0)B) Calculate the velocity of the marble at B.C) Calculate the velocity of the marble at C

A

C

B

10m

3m

Ex. 6-11 Dart Gunmdart = 0.1kgk = 250n/mx = 6cmFind the velocity of the dart when it releases from the spring at x = 0.

A marble having a mass of 0.2 kg is placed against a compressed spring as shown below. The spring is initially compressed 0.1m and has a spring constant of 200N/m. The spring is released. Calculate the height that the marble rises above its starting point. Assume the ramp is frictionless.

h

Nonconservative Forces

• 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.

• Examples of nonconservative forces– kinetic friction, air drag, propulsive forces

• Examples of conservative forces– Gravitational, elastic, electric

Power• Often also interested in the rate at which the

energy transfer takes place• Power is defined as this rate of energy transfer

– SI units are Watts (W)

2

2

s

mkg

s

JW

P = W = FΔx = Fvavg

t t

Power, cont.

• US Customary units are generally hp– need a conversion factor

– Can define units of work or energy in terms of units of power:

• kilowatt hours (kWh) are often used in electric bills

W746s

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