AP Physics C I.C Work, Energy and Power

Amazingly, energy was not incorporated into physics until more than 100 years after Newton.

Still a good definition for energy – “ Energy is the capacity to do work”

And if the force is constant, we have our old friend... W = Fd cos θ

A note on the sign of work When 0º ≤ θ < 90º work is positive When θ = 90º work is zero When 90º < θ ≤ 180º work is negative

Ex. A book with a mass of 2.0 kg is lifted at a constant velocity to a height of 3.0 m. How much work is done on the book?

Ex. A 15 kg crate is moved along a horizontal surface by a warehouse worker who is pulling on it with a rope that makes an angle of 30.0° with the horizontal. The tension in the rope is N and the crate slides a distance of 10.0 m. a) How much work is done on the crate by the rope? b) How much work is done on the crate by the normal force? c) How much work is done on the crate by the frictional force if the coefficient of kinetic friction is 0.40?

Ex. A box slides down an inclined plane that makes an angle of 37° with the horizontal. The mass of the block is 35 kg, the coefficient of friction between the box and ramp is 0.30 and the length of the ramp is 8.0 m. How much work is done by a) gravity? b) the normal force? c) friction? d) What is the total work done?

Graphing work vs. displacement

A quick review of Hooke’s Law

Ex. What is the work done on a spring that is stretched from equilibrium (x = 0) to final displacement x?

Note: the previous example used the calculus form for work since the force was not constant (it was a function of displacement)

The (net) Work (kinetic) Energy Theorem ΣW = ΔK

Ex. Use the work-kinetic energy theorem to find the height a tennis ball with mass (0.06 kg) would reach if it is hit upward with an initial speed of 50.0 m/s. Air resistance is negligible.

Ex. From the box in the previous example (ΣW = 1020 J), if the box starts from rest at the top of the ramp, with what speed does it reach the bottom?

Ex. A pool cue striking a stationary billiard ball (mass of 0.25 kg) gives the ball a speed of 2.0 m/s? If the average force on the cue on the ball was 200 N, over what distance did this force act?

Potential Energy – energy an object has because of its configuration within a system. If the configuration changes, the potential energy changes.

Relationship between change in potential energy and work (important: if the field does work, the potential energy of the object decreases. That energy has been converted to kinetic energy.)

Gravitational Potential Energy U g = mgh

Conservation of Mechanical Energy (makes lots of problems simple that might otherwise be horrendous)

Ex. A child of mass m starts from rest at the top of a water slide 8.5 m above the bottom of the slide. Assuming the slide is frictionless, what is the child’s speed at the bottom of the slide?

Note: if no non-conservative forces (friction, tension, air resistance) are present, the change in energy is independent of the path taken. Gravity is a conservative force.

Ex. A box, with an initial speed of 3.0 m/s, slides up a frictionless ramp that makes an angle of 37° with the horizontal. How high up the ramp will the box slide? What distance along the ramp will it slide?

Ex. A skydiver jumps fro a hovering helicopter that is 3000 m above the ground. If air resistance is negligible, how fast will the skydiver be falling when his altitude is 2000 m?

Modifying conservation of energy to include non- conservative forces

Ex. Wile E. Coyote (mass = 40 kg) falls off a 50 m high cliff. On the way down, the average force of air resistance is 100 N. Find the speed with which he crashes into the ground.

Ex. A skier starts from rest at the top of a 20.0° incline and skis in a straight line to the bottom of the slope a distance d (measured along the slope) of 400 m. If the coefficient of kinetic friction between the skis and the snow is 0.20, calculate the skier’s speed at the bottom of the run.

Potential Energy Curve

Key aspects of a potential energy curve The object moves in a linear path along + x and –x-axis The force is the negative slope of the curve E mec = U(x) + K(x) Turning points: locations where the object is at rest; i.e. K(x) = 0 and E mec = U(x) Object is in equilibrium (neutral, unstable, stable) when slope = 0 (F(x) = 0) Object cannot reach locations where K is negative To graph: graph zeros (F(x) = 0), regions of constant force and connect.