Work Power and Kinetic Energy Work Work is

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

Work • If the force is at an angle to the displacement:

Work

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

• If on by by Work there is more than one force acting an object, we can find the work done each force, and also the work done 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) = 129. 9 Joules

Question • A tired squirrel (mass of 1 kg) does pushups 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. • Wapp = (10 N) * (5 m) * cos (0 deg) = +50 Joules • Wfrict = (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

Wheel of Pain • If the radius of the wheel is 8 meters and it takes 12000 N 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. vf 2= vi 2 + 2 aΔx an equation of motion 3. vf 2 -vi 2 = 2(F/m)Δx Use equation 1 and 2 4. ½ mvf 2 - ½ mvi 2 = ½ m *2(F/m)Δx • multiply all terms by ½ mvf 2 - ½ mvi 2 = FΔx = Work ½ mvf 2 - ½ mvi 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 107 J • What happens if you double the speed?

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