C H A P T E R 1 0
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