physics 504 chapter 15 simple machines
Post on 18-Dec-2014
1.067 Views
Preview:
DESCRIPTION
TRANSCRIPT
Energy and its TransformationsSimple Machines,
Work & Power
Chapter 15
Examples
Simple Machines and Work
• A simple machine is a device used to make work easier.
• It is used to multiply forces or change the direction of the force.
• No machine is 100% efficient.• Energy is always lost to friction.• The person must do more work, but easier
work, i.e. less force.• A lesser force is applied over a greater
distance.
Definitions & Equation
• Effort Force, FE: Force used by person, N
• Effort Distance, ΔdE: Distance person’s force is applied over, m.
• Resistance Force, FR: Force that comes from machine, or weight of object, N
• Resistance Distance, ΔdR: Distance object is moved, m.
• FE x ΔdE = FR x ΔdR
Mechanical Advantage
• Mechanical Advantage is a measure of how much easier the task has become.
• Ideal Mechanical Advantage – no friction:• IMA = ΔdE = Effort arm length ΔdR Resistance arm length• Actual Mechanical Advantage – with friction.• AMA = FR
FE
Levers
• The fulcrum is a pivot that can act to change the direction and magnitude of the force.
• Depending on force direction and position of fulcrum:– 1st class– 2nd class– 3rd class
1st Class Lever
• 1st Class Lever: The fulcrum, or pivot, is located between the 2 forces.
• E.g. lever, seesaw, teeter-totter, scissors.
2nd Class Lever
• 2nd Class Lever: The fulcrum is located on 1 side of both forces.
• E.g. wheel barrow, nutcracker
3rd Class Lever
• 3rd Class Lever: The effort force is between the resistance force and the fulcrum.
• E.g. tweezers, hockey stick
Variations of the Lever• The pulley is a variation of the lever.
• IMA = the number of supporting ropes.
• IMA = ΔdE
ΔdR
• AMA = FR
FE
Wheel and Axle
• The wheel and axle acts like a 2nd class lever. E.g. doorknob, taps, steering wheel
• IMA = radiusE AMA = FR
radiusR FE
The Inclined Plane
• The inclined plane trades distance for force by reducing the force needed to work against gravity.
• E.g. stairs, ramps, screw
Inclined Plane Formula
• IMA = length of slope = ΔdE
height of slope ΔdR
• AMA = FR = mg
FE FE
Activity
• A 1st class lever has a AMA of 4. How much force is needed to lift 5 kg?
• AMA = FR = mg
FE FE
• 4 = 5kg x 9.81 m/s2
FE
• FE = 12.25 N
Exam QuestionA workman uses a pulley to lift a 50 kg sack of potatoes by pulling downwards on a rope with a force of 550 N.
x
What is the acceleration of the sack? A)
1.0 m/s2
B)
2.1 m/s2
C)
4.5 m/s2
D)
11 m/s2
Measuring Work
• Work is defined as the energy that comes from applying a force over a certain distance.
• W = F Δd = mad (horizontal)
• = magd (against gravity)
• Work is in Joules, J
• Force is in Newtons, N
• Distance is in metres, m
Activity
• E.g How much work is done by a boy pushing a car with a force of 800 N over a distance of 200m?
• W = F d
• = 800 N x 200 m
• = 160 000 J = 160 kJ
• Do page 330, Q. 1-4
Exam QuestionA 200 g brick falls from a wall 4.0 metres above the ground. It hits the ground with a velocity of 8.5 m/s.
4.0 m
How much work did gravity do on the brick?
A)
8.0 J
B)
7.2 J
C)
3.4 J
D)
1.7 J
Exam QuestionA sled has a mass of 10 kg. A child pulls the sled a distance of 20 metres with a force of 10.0 N at an angle of 35° with respect to the horizontal. During this motion, a force of friction of 4.0 N acts in the opposite direction of the motion.
35
10.0 N
How much work is done on the sled by the child over the distance of 20 metres?
A)
1.6 102 J
B)
1.1 102 J
C)
8.4 101 J
D)
3.5 101 J
Efficiency
• The IMA is always greater than the AMA.
• The MA must be greater than 1.
• % Efficiency = Work output x 100 = AMA
Work input IMA
• The maximum efficiency is 100%.
• It is a measure of what energy is lost to friction, vibration, and other factors.
Power
• Power is defined as the rate at which work is being done.
• P = W
• Δt
• Work is in Joules,
• Time is in seconds
• Power is in Watts
Activity
• What is the power of a bulldozer that does 55000J of work in 1.1s?
• P = W = 55000J = 50000 Watts
Δt 1.1s
• If 100000 J of energy was expended by the bulldozer, what is its efficiency?
• Do page 334, Q 1-5
Exam Question
A horse is hitched up to a buggy with a mass of 500 kg including the people inside. Disregard the effects of friction. Starting from rest, the horse exerts a horizontal force of 300 newtons on the buggy over a distance of 30 metres. What is the average power that the horse develops over the first 30 metres?
A)
9.0 102 W
B)
9.0 103 W
C)
4.5 105 W
D)
4.5 106 W
Summary
• Work done on object equals the applied force times the displacement of the object in the direction of the force.
• W = FΔd• The units are Joules, J, or Nm.• Power is the rate at which work is done
per unit of time.• P = W/Δt• The units are Watts, W, or J/s
Summary
• The Efficiency of a machine is given by the formula, Efficiency = Work output x 100
Work input• A machine is supposed to reduce the force
required by a person to do a physical task.• Ideal Mechanical Advantage does not take
into account friction.• IMA = effort distance • resistance distance
Summary
• Actual Mechanical Advantage, AMA, takes friction into account.
• AMA = Resistance Force
Effort Force
Exam Question
A car with a mass of 1000 kg and moving at a speed of 30 m/s comes to rest over a distance of 100 metres. What is the force of friction (acting on the wheels of the car) which causes the car to stop?
A)
3 000 N
B)
3 500 N
C)
4 000 N
D)
4 500 N
Activity
• Do Page 338, Q. 1-6
top related