Reading Quiz - Work & Energy 1. A woman holds a bowling ball in a fixed position. The work she does on the ball ___ 1. depends on the weight of the ball. ___ 2. cannot be calculated without more information. ___ 3. is equal to zero.
2. A man pushes a very heavy load across a horizontal floor. The work done by gravity on the load ___ 1. depends on the weight of the load. ___ 2. cannot be calculated without more information. ___ 3. is equal to zero.
3. When you do positive work on a particle, its kinetic energy ___ 1. increases. ___ 2. decreases. ___ 3. remains the same. ___ 4. need more information about the way the work was done
4. The gravitational potential energy of a particle at a height z above Earth’s surface ___ 1. depends on the height z. ___ 2. depends on the path taken to bring the particle to z. ___ 3. both 1 and 2. ___ 4. is not covered in the reading assignment.
5. Which of the following is not a conservative force? ___ 1. the force exerted by a spring on a particle in one dimension ___ 2. the force of friction ___ 3. the force of gravity ___ 4. not covered in the reading assignment
Work • Work done by a constant force on an object: where F = magnitude of constant force d = magnitude of the displacement = angle between the force and displacement vectors
Graphical interpretation of work • Work done by a variable force.
Conceptual Questions 1) A box slides through a distance of 3 m on a rough floor where the force of friction is 10 N. What is the work done on the box? ____ a) 0 N·m ____ b) +30 N·m ____ c) - 30 N·m ____ d) +0.30 N·m ____ e) - 0.30 N·m
2) The moon revolves around the earth in a circular orbit, kept there by the gravitational force exerted by the earth. Gravity does ___ a) positive work ___ b) negative work ___ c) no work ___ d) variable work on the moon. What evidence do you have to support your answer?
3) The figure shows four situations in which a force acts on a box while the box slides to the right a distance d across a frictionless floor. The magnitudes of the forces are identical. Rank the situations according to the work done on the box during the displacement, from most positive to most negative.
Quantitative Questions 1) Find the work done by the force of gravity when an object of mass m is raised from a height of y meters to a height of y+h meters. 2) A spring is a device where the force it exerts is directly proportional to its displacement from its natural (unstretched) length. The constant of proportionality is called the spring constant k. Draw a graph of the spring force versus its displacement. What is the work done in stretching a spring from its natural length by an amount x?
3) A 280 kg piano slides 4.3 m down a 30 incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. The effective coefficient of kinetic friction is 0.40. Calculate: (a) the force exerted by the man, (b) the work done by the man on the piano, (c) the work done by the friction force, (d) the work done by the force of gravity, and (e) the net work done on the piano.
Energy • Energy - property that gives something the capacity to do work. Three broad categories: - Kinetic energy - Potential energy - Rest energy • Kinetic Energy - Energy related to motion: (definition) • Potential Energy - Energy related to position. • Rest Energy - Energy by virtue of the mass of an object:
Work-Energy Principle • The net work done on an object is always equal to the change in its kinetic energy: • Conservative forces: work done by these forces are independent of path; they depend only on the end points. Examples include gravitation, spring and magnetic forces. • It is meaningful to define an associated potential energy only for conservative forces.
Quantitative Problems 1) An automobile traveling 60 km/h can brake to a stop within a distance of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping distance? The maximum braking force is approximately independent of speed. 2) A 600 gram hammer head strikes a nail at a speed of 4.0 m/s and drives it 5.0 mm into a wooden board. What is the average force on the nail?
3) A crate of mass 10 kg is pulled up a rough incline with an initial speed of 1.5 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 20° with the horizontal. If the coefficient of kinetic friction is 0.4, and the crate is pulled a distance of 5 m, (a) how much work is done against gravity? (b) How much work is done against friction? (c) How much work is done by the 100 N force? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5 m?
Potential Energy • For every conservative force, we can define a potential energy function. The change in the potential energy is equal to the negative of the work done by the conservative force: • Examples: gravitational PE = mgh elastic PE = • Note: Cannot define a potential energy function for a non-conservative force.
Conservation of Mechanical Energy • Net work done by net force which equals the vector sum of conservative and non-conservative forces, implying: • Since , and , the above reduces to: - the general form of the work-energy principle. • If only conservative forces are acting, or if the work done by the non-conservative forces present is zero, i.e. , then
Conceptual Question Two water slides at a pool are shaped differently but start at the same height h. Two riders, Paul and Kathleen, start from rest at the same time on different slides.
Which rider, Paul or Kathleen, is travelling faster at the bottom and who gets there first? ___ a) Paul & Paul ___ e) same & Paul ___ b) Paul & Kathleen ___ f) same & Kathleen ___ c) Kathleen & Paul ___ g) Paul & same ___ d) Kathleen & Kathleen ___ h) Kathleen & same
Quantitative Problems 1) A small mass m slides without friction along the looped apparatus show. If the object is to remain on the track, even at the top of the circle (whose radius is r), from what minimum height h must it be released?
2) A roller coaster is pulled up to point A where it is released from rest. Assuming no friction, calculate the speed at points B, C and D. Now suppose the roller coaster passes point A with a speed of 1.70 m/s. If the average force of friction is equal to one fifth of its weight, with what speed will it reach point B? The distance traveled is 45.0 m.
3) A ball is attached to a horizontal cord of length L whose other end is fixed. (a) If the ball is released, what will be its speed at the lowest point of its path? (b) A peg is located a distance h directly below the point of attachment of the cord. If h= 0.80L, what will be the speed of the ball when it reaches the top of its circular path about the peg?
4) The figure shows an 8 kg stone at rest on a spring. The spring is compressed 10.0 cm by the stone. (a) What is the spring constant? (b) The stone is pushed down an additional 30.0 cm and released. What is the elastic potential energy of the compressed spring just before that release?
(c) What is the change in the gravitational potential energy of the stone-Earth system when the stone moves from the release point to its maximum height? (d) What is that maximum height, measured from the release point?
Conservation of Energy; Power • The law of conservation of energy is one of the most important principles of physics. It states: The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one body to another, but the total amount remains constant. • Power: rate of doing work (or transforming energy). Hence average power is
Discussion Problems 1) Other than nuclear energy, why do we say the source of all energy comes from the sun? Specifically, what about: (a) wind energy (b) hydro-electricity (c) fossil fuel - coal, wood, oil, gas (d) food that we eat
2) To accelerate your car at a constant acceleration, the car’s engine must ____ a) maintain a constant power output ____ b) develop ever-decreasing power ____ c) develop ever-increasing power ____ d) maintain a constant turning speed
3) Compared to yesterday, you did 3 times the work in one-third the time. To do so, your power output must have been ____ a) the same as yesterday’s power output ____ b) one-third of yesterday’s power output ____ c) 3 times yesterday’s power output ____ d) 9 times yesterday’s power output