Download Chapter 6 Notes

AP Physics 1 Chapter 6 Notes
Section 6-1 Work done by a constant force
Work – what is accomplished when a force is applied to an object to move it over a distance
The work done on an object by a constant force (constant in both magnitude and direction) is
defined to be the product of the magnitude of the displacement times the component of the
force parallel to the displacement.
EQUATION FOR WORK
Units of Work: ___________________
Scenario # 1 – The force is in the same direction as the displacement
Scenario # 2 – The force is in the opposite direction of the displacement
Scenario # 3 – The force is at an angle with respect to the displacement.
Can a force be exerted on an object and no work be done on the object?
Problems solving strategies for Work
1. Draw a free body diagram.
2. Choose a convenient coordinate system. (Usually it is convenient to choose the
direction of motion).
3. Apply Newton’s Laws to determine any unknown forces.
4. Find the work done by a specific force on the object.
5. To find net work: (a) find the work done by each force and add the results algebraically
(b) find the net force on the object and apply it using Wnet = Fnet d cosϴ
Examples...
(1) How much work is done on a bag of groceries carrying them to your car? (assume flat
ground)
(2) How much work is done carrying a bag of groceries up a ladder? (Not sure why you woul
d carry them up a ladder!)
(3) A person pulls a 50-kg crate 40 meters along a horizontal floor by a constant force Fp =
100 N, which
acts at a 37 degree angle. The floor is rough and exerts a friction force Ffr = 50 N. Deter
mine (a) the
work done by each force acting on the crate, and (b) the net work done
the crate.
(4) The work done on a backpack (a) Calculate the work a hiker must do on a backpack of
mass m = 15 kg in order to carry it up a hill of height h = 10 m, as shown. (b) Calculate
the work done by gravity on the backpack. (c) Calculate the net work done on the
backpack.
(5) The Moon revolves around the Earth in a nearly circular orbit, with approximately
constant tangential speed, kept there by the gravitational force exerted by the Earth. Does
gravity do
(a) positive work
(b) negative work, or
(c) no work at all on the Moon?
Section 6-2 Work Done by Varying Force
The work done by a varying force can be determined graphically. If you plot F vs d, then the
work is the area under the curve at the two points.
The force on an object, acting along the x axis, varies as shown above. Determine the work
done by this force to move the object (a) from 0.0m to 10.0m and (b) from 0.0m to 15.0 m.
Section 6-3 Kinetic Energy/Work-Energy Principle
• Energy: Traditionally defined as the ability to do work. We now know that not all forces
are able to do work; however, we are dealing in these chapters with mechanical energy,
which does follow this definition.
• Kinetic Energy :The energy of motion
• An object in motion has the ability to do work.
• The net work done by a constant force in accelerating an object of mass m from v1 to v2
is
KE.
• Kinetic Energy (KE) = ½ mv2
• units are Joules, J
• Work-energy principle: Wnet = KE
Examples….
(1) A baseball, mass m = 145 g (0.145 kg) is thrown so that it acquires a speed v = 25 m/s.
a. What is its kinetic energy?
b. What was the net work done on the ball to make it reach this speed, starting from
rest?
(2) Calculate the net work required to accelerate a car, mass m = 1000-kg car from v1 = 20
m/s to v2 = 30 m/s.
(3) A car traveling at speed v1 = 60 km/h can brake to a stop within a distance d = 20 m. If
the car is going twice as fast, 120 km/h, what is its stopping distance? Assume that the
maximum braking force is approximately independent of speed.
Section 6-4 and 6-5
An object can have potential energy (U) by virtue of its surroundings.
Familiar examples of potential energy: A wound-up spring, a stretched elastic band, an object
at some height above the ground
Gravitational potential energy: potential energy due to its position relative to the Earth
Gravitational PE equation
Where do we measure h from? It turns out not to matter, as long as we are consistent about
where we choose h = 0. Only changes in potential energy can be measured.
Example:
A 1000. Kg roller-coaster car moves from point 1 to point 2 and then to point 3. (a) What is
the gravitational potential energy at point 2 and point 3 relative to point 1? That is, take y=0
at point 1. (b) What is the change in potential energy when the car goes from point 2 to point
3?
Elastic PE: Potential energy stored in elastic materials as the result of their stretching or
compressing.
Elastic PE equation
Section 6-6, 6-7, 6-8 Mechanical Energy and its Conservation
We can distinguish between the work done by conservative forces (not dependent of path
taken) and the work done by nonconservative (dependent on path taken) forces.
We find that the work done by nonconservative forces is equal to the total change in kinetic
and potential energies:
Work Energy Principle for nonconservative forces:
Mechanical energy: potential or kinetic energy
If a system has only conservative forces acting on it, then the conservation of mechanical
energy states: the mechanical energy of the system is constant.
Simply put: the energy of the system anywhere on its path is constant, the only thing that may
change is the type of energy involved.
Conservation of Mechanical Energy formula
Examples:
If the original height of the stone is 3.0 m, calculate the stone’s speed when it has fallen to 1.0
m above the ground.
If the roller coaster car is pulled up to point 1, starts from rest and coasts down the track, what
will its speed be at point 4? Assume no friction between the car and track and no air drag.
A dart of mass 0.100 kg is loaded in a toy dart gun. The spring in the gun has a spring constant
of 250 N/m. The spring is compressed 6.0 cm and then released. What speed does the dart
leave the gun with?
A 1.60 kg block slides with a speed of 0.950 m/s on a frictionless, horizontal surface until it
encounters a spring with a force constant of 902 N/m. The block comes to rest after
compressing the spring 4.00 cm. Find the spring potential energy, U, the kinetic energy of the
block, K, and the total mechanical energy of the system, E, for the following compressions: 0
cm, 2.00 cm, 4.00 cm.
A 1.75-kg rock is released from rest at the surface of a pond 1.00 m deep. As the rock falls, a
constant upward force of 4.10 N is exerted on it by water resistance. Calculate the
nonconservative work, Wnc, done by the water resistance on the rock, the gravitational
potential energy of the system, U, the kinetic energy of the rock, K, and the total mechanical
energy of the system, E, for the following depths below the water’s surface: d = 0.00 m, d =
0.500 m, d = 1.00 m. Let potential energy be zero at the bottom of the pond.
A ball of mass m = 2.60 kg, starting from rest, falls a vertical distance h = 55.0 cm before
striking a vertical coiled spring, which it compresses an amount Y = 15.0 cm. Determine the
spring constant. Assume the spring has negligible mass, and ignore air resistance.
6-10
• Power  The rate at which work is done or the rate at which energy is transformed.
• Average Power:
P = (Work)/(Time) = (Energy)/(time)
SI units: Joule/Second = Watt (W) 1 W = 1J/s
British units: Horsepower (hp). 1hp = 746 W
“Kilowatt-Hours” (from your power bill). Energy!
1 KWh = (103 Watt) ·(3600 s) = 3.6 X 106 W s = 3.6 X 106 J
Power Formulas:
Examples:
1. A 60-kg jogger runs up a flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m.
a. Estimate the jogger’s power output in watts and horsepower.
b. How much energy did this require?
2. An elevator car of mass 1,600 kg, carries people, mass of 200 kg. A constant friction force of
4,000 N acts against the motion. Find the power needed for a motor to lift the car +
passengers at a constant velocity v = 3 m/s.
Calculate the power required of a 1400-kg car to do the following: Assume that the average
retarding force on the car is FR = 700 N.
a. Climb a 10° hill (steep!) at a steady 80 km/h
b. Accelerate on a level road from 90 to 110 km/h in 6.0 s
Efficiency