Work, Power and Kinetic Energy

Work Work is a force acting through a distance In order for work to be done: –The object the force is applied to must move –The movement must be in the same direction as the force being applied

Is There Work Done? A teacher applies a force to a wall and becomes exhausted. A book falls off a table and free falls to the ground. A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed.

Answers This is not an example of work. The wall is not displaced. A force must cause a displacement in order for work to be done. This is an example of work. There is a force (gravity) which acts on the book which causes it to be displaced in a downward direction (i.e., "fall"). This is not an example of work. There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

Work Work = Force x Distance Label work using the joule (J). 1 joule (J) = 1 Newton x 1 meter (Force) (Distance)

Work

If you pull a ridiculously large granite block weighing 130,000 N a distance of 100 meters to the base of the pyramids how much work do you do? Assume you pull at the absolute minumum force which equals the force of kinetic friction. Coefficient of kinetic friction =.8

Work

If the force is at an angle to the displacement:

Work

The work done may be positive, zero, or negative, depending on the angle between the force and the displacement:

Work If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force

Question A force of 50 N acts on the block at the angle shown in the diagram. The block moves a horizontal distance of 3.0 m. How much work is done by the applied force? W = F * d * cos(θ) W = (50 N) * (3 m) * cos (30 degrees) = Joules

Question A tired squirrel (mass of 1 kg) does push- ups by applying a force to elevate its center-of-mass by 5 cm. Estimate the number of push-ups which a tired squirrel must do in order to do a approximately 5.0 Joules of work.

Question A 10-N force is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m to the right. W app = (10 N) * (5 m) * cos (0 deg) = +50 Joules W frict = (10 N) * (5 m) * cos (180 deg) = -50 Joules

Graphing Constant Force Variable Force

Power Power is the rate at which work is done. Power = Work Time OR Power = Force x Distance Time

Wheel of Pain

If the radius of the wheel is 8 meters and it takes 12000N of force to move it how much work does Conan do every rotation?

Tree of Woe

Power Power is measured in the unit called a watt (W) 1 watt = 1 joule per sec (1 J/sec) Power = Work (joule) Time (sec)

Horsepower 746 watts – 1 Horsepower Literally based off of the power of horses

7-2 Kinetic Energy and the Work-Energy Theorem When positive work is done on an object, its speed increases; when negative work is done, its speed decreases.

7-2 Kinetic Energy and the Work-Energy Theorem

Why does ΔK = work? 1.F = ma 1.a = F/m 2.v f 2 = v i 2 + 2aΔx an equation of motion 3.v f 2 -v i 2 = 2(F/m)Δx Use equation 1 and 2 4.½ mv f 2 - ½ mv i 2 = ½ m *2(F/m)Δx multiply all terms by ½ m ½ mv f 2 - ½ mv i 2 = FΔ x FΔx = Work ½ mv f 2 - ½ mv i 2 = Work

Determine the kinetic energy of a 625-kg rocket powered rail car that is moving with a speed of 312 m/s. Answer: 3.0 x 10 7 J What happens if you double the speed?

Springs F = kxHooke’s Law Work = F*d Work from a spring = ½ kx*x Work = ½ kx 2