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ENERGY, WORK AND SIMPLE MACHINES

ENERGY AND WORK

• How do we define the relationship between work and energy?

• How can we calculate work done?

• How do we calculate power used?

WORK EQUATION

• Previous chapter: change in momentum is due to an impulse

• Impulses are force multiplied by time

• The force creates an acceleration ()

• If we put his acceleration into a kinematic equation and do some algebra…

WORK EQUATION

• Recognize left side?

• is Kinetic Energy!

• Energy: the ability of an object to produce a change in itself or the world around it

• Whole left side is change in kinetic energy

WORK EQUATION

• Right side is Fd

• F = force (in Newtons)

• d = distance (in meters)

• We define:

• W = Fd

• Work = forces times distance

WORK ENERGY THEOREM

• Work-Energy Theorem: When work is done by an object, the result is a change in kinetic energy

• This relationship was discovered by James Prescott Joule

• Unit of energy is a Joule (J)

• 1 Joule = 1 Newton meter = 1 kg·m2/s2

EXAMPLE

• A 105 g hockey puck is sliding across the ice. A player exerts a constant 4.50 newton force over a distance of 0.150 m. How much work does the player do on the puck? What is the change in energy?

LIFTING A BOOK

• When is the work positive?

• When is the work negative?

• When is the work zero?

WORK AGAINST GRAVITY

• W = Fd

• The work of lifting something is equal to the weight of the object times the distance lifted

• Weight =

• So W =

WORK

• Since work equals the change in KE, the unit is the same

• Work is measured in joules

• One joule happens when a force of 1 N acts for 1 m

• An apple is approximately a newton, so lifting an apple 1 meter is about 1 Joule of work

WORK

• What if our force is not applied in a straight line?

• Will it be as effective?

• How do we account for this?

WORK

• W = Fdcosɵ

• ɵ is between the force and the direction of displacement

• If he pushes the car 10.0 m, how much work did the man do?

WHAT TO INCLUDE IN WORK

• Which direction do the normal force and gravity point?

• ɵ is …

• What about friction?

EXAMPLE

• A sailor pulls a boat a distance of 30.0 m along a dock using a rope that makes a 25.0° angle with the horizontal. How much work does the sailor do on the boat if he exerts a force of 255 N on the rope?

TRIG REFRESHER

• SOH-CAH-TOA

WORK AGAINST GRAVITY

• Pushing up a ramp, walking up stairs

• What do we use for d?

HOMEWORK

• Page 287, # 1 – 3• Page 291, # 4 - 8

GRAPHICAL METHOD

• Area under force vs displacement curve is work

• How much work?

GRAPHICAL METHOD

• Force exerted by a spring

• Work =

• Area of a trapezoid= • ½ h (b1 + b2)

MULTIPLE FORCES

• If several forces are exerted on a system, calculate the work done by each force, then add the results

POWER

• Power: work done divided by the time to do the work

• Unit = Joules per second = watt

• Since watts are so small, kilowatts are often used

POWER

• Three student going up stairs

• If they started at the same time…

• How does their work compare?

• How does their power compare?

POWER

• On a ten-speed bike, there is a combination of force and speed that will produce the maximum power

EXAMPLE

• An electric motor lifts an elevator 9.00 m in 15.0 s by exerting an upward force of 1.20 x 104 N. What power does the motor produce in kW?

HOMEWORK

• Page 264, # 9 – 14• Page 265, # 15 - 21