Example : Mr. Clean – A man pulls on his vacuum cleaner at an angle of 30.0 degrees with the force of 50.0 N for a distance of 3.00 m. How much work does he do on the vacuum cleaner?
Ex. Find the work required to raise a bucket that weighs 250 N a distance of 0.80 m if the bucket is raised at a constant velocity. What is the work required to lower the bucket?
Summary If the force and displacement are in the same direction, work is positive (cos 0º = 1) If the force and displacement are in opposite directions, work is negative (cos 180º = –1) If the force and displacement are perpendicular, work is zero (cos 90º = 0) Be sure and note the force which does the work (ex. applied force, friction, net force)
Ex. A 15 kg crate is moved along a horizontal floor by a warehouse worker who pulls on it with a rope that makes an angle of 30.0º with the horizontal. The tension in the rope is 69 N and the crate slides a distance of 10 m. How much work is done on the crate by the worker? If the coefficient of kinetic friction between the crate and floor is 0.40, how much work is done by the normal force? How much work is done by the frictional force?
Ex. A box slides down a ramp that makes an angle of 37.0º with the horizontal. The mass of the block is 35 kg, the coefficient of kinetic friction between the ramp and box is 0.30 and the length of the ramp is 8.0 m. a) How much work is done by gravity? b) How much work is done by the normal force? c) How much work is done by friction? d) What is the total work done on the box?
Ex. A force applied to an object increases at a constant rate from 0.0 N to 15.0 N while the object is pushed a distance of 5.0 m. The force then decreases at a constant rate to 0.0 N while the box is pushed an additional 10.0 m. Graph the motion on a force vs. distance graph and find the net work done on the object.
The Work-Energy Theorem And now, to the amazement of everyone, I shall prove to you once and for all...
Ex. How much work is required to accelerate a 1.00 EE 3 kg car from an initial speed of 20.0 m/s to 30.0 m/s?
Ex. A net force of 4500 N is applied to a 1400 kg car that is initially at rest. What is the kinetic energy and speed of the car after it has traveled 1.0 EE 2 m?
Ex. A pool cue striking a stationary billiard ball (mass 0.25 kg) gives the ball a speed of 2.0 m/s. If the average force on the cue ball was 200 N, over what distance did this force act?
The work-energy theorem applies to work done by a net external force, not an individual force. If the work done by the net force is positive, K increases. If the work done by the net force is negative, K decreases.
A ball falls from a tall wall of a stall in the hall of the mall and is observed by a man named Paul.
Ex. A pole vaulter clears a cross bar at a height of 4.2 m. If the vaulter is momentarily at rest at the height of the bar, what is the speed as she lands in the pit directly below the bar?
Ex. A Big Mac is thrown horizontally with a speed of 15.0 m/s from a 20.0 m high cliff. What is the speed of the Big Mac when it is 8.0 m above the ground?
Ex. A baboon on a vine is released from rest (by an elephant that holds the vine with its trunk) when the vine makes an angle of 35º with the vertical. The length of the vine is 3.0 m. What is the speed of the baboon as it swings through the lowest point of its circular arc?
Ex. A Viking and a sled have a combined weight of 8.00 EE 2 N. If he slides on the sled down a frictionless hill a vertical distance of 10.0 m, find the speed at the bottom of the hill if the Viking pushes off with an initial speed of 5.00 m/s.
Ex. An overbaked chocolate cake, with a mass of 3.5 kg rests on a frictionless table and compresses a spring with a spring constant of 25 N/m a distance of 0.20 m. The cake is released by a hungry humanoid. What maximum speed does the cake attain?
Ex. a) A box of mass 2.0 kg is released from rest and slides down a frictionless inclined plane of height 0.5 m. The box compresses a spring at the bottom of the ramp with spring constant of 200 N/m. How far does the box compress the spring? b) If the box and compressed spring are placed in a position such that the box is free to move at the edge of a frictionless table, how fast is the box moving when the box is released from rest? c) Suppose the table is 0.80 m high. How far from a point directly below the edge of the table will the block strike the floor?
Ex. A catfish with a mass of 2.0 kg compresses a vertical spring a distance 0.25 m. If the catfish is released from rest, and the spring constant is 300 N/m, what is the maximum vertical height attained by the catfish?
Mechanical energy, potential energy, kinetic energy graphs (energy vs. time and energy vs. distance)