Work and Energy

Work

Physics definition of Work:

Work : is the product of the magnitudes of the component of force along the direction of displacement and the displacement

W = Fd

F=ma

W = m a d

W = workF = forceD = displacement

Work

Work is done only when components of a force are parallel to a displacement.

disp

lace

men

t

force

WORK!force

displacementNO WORK!

Is Work Happening?

A tug of war that is evenly matched A student carries a bucket of water along a

horizontal path while walking at a constant velocity.

A Crane lifting a car. A person holding a heavy chair at arm’s

length for several minutes. A train engine pulling a loaded boxcar initially

at rest.

Work Units

Work = F x d

Work = m x a x d

Work = (newtons) (m)

(Newton x m) = joules (J)

Work Problem 1

A tugboat pulls a ship with a constant horizontal net force of 5.00 x 103 N. How much work is done if the ship is pulled a distance of 3.00 km?

W = F x d

= 5.00 x 10 3 N ( 3000 m)

= 1.5 x 107 Nm or J

Work Problem 2

If 2.0 J of work is done raising a 180 g apple, how far is it lifted?

W =FdF = mg = 0.18kg(9.8 m/s2) = 1.76 NW = Fd2 J = (1.76N)dd = 1.1 m

Work Problem 3

A weight lifter lifts a set of weights a vertical distance of 2.00 m. If a constant net force of 350 N is exerted on the weights, what is the net work done on the weights?

W = FdW = 350 N x 2.00 m = 700 Nm or 700J

Sample Problem 4

What work is done by a forklift raising 583 kgs of frozen turkeys 1.2 m?

W = Fd

F = 583 kg (9.8 m/s2) = 5713.4 N

W = 5713.4 N ( 1.2m) = 6856 Nm or 6856 J

Problems with Forces at Angles

θ

F

Fx = Fcos θFy = Fsin θ

Because the displacement of the box is only in the x direction only the x-component of the force does work on the box.

W = Fdcosθ

X-direction

Sample Problem

A sailor pulls a boat a distance of 30.0 m along a dock using a rope that makes an angle of 25o with the horizontal. How much work is done if he exerts a force of 255 N on the rope?

255 N

250

W = Fdcosθ = 255N(30m)cos25 = 6.93 x 103J

Sliding up an Incline

What we calculated was... For sliding an object up an incline..

W = Fd

W = (mg sinθ) d

Sample Problem

An airline passenger carries a 215 N suitcase up stairs, a displacement of 4.20 m vertically and 4.60 m horizontally. How much work does the passenger do?

4.6 m

4.2 m

Sample Problem

4.6 m

4.2 mFirst have to calculatehypotenuse and θ

Tan θ = 4.2 m/ 4.6 mΘ = 42.40

Hypotenuse2 = A2 + B2

Hypotenuse2 = (4.2)2 + (4.6)2

Hypotenuse = 6.23 m

42.40

6.23 m

Sample Problem

4.6 m

4.2 m

6.23 m

42.40

F║ = mg sinθ = 215 sin 42.4 = 145 N

W = Fd = 145 N ( 6.23 m) = 899 Nm = 903 J

This should equal the force of the suitcase moving itvertically 4.2 m W = 215 N ( 4.2 m) = 903 J

Suitcase weighs 215 N

Graphs of Force vs. Displacement

Displacement

Fo

rce

Displacement

Fo

rce

Work = FdWork can be found graphically by finding thearea under the curve

Homework

Do Work/Energy/Power worksheet #1-4