Work, Power & Energy

Work

• Work is the product of force and distance– For a force to do work on an object, some

of the force must act in the same direction as the object moves. If there is no movement, no work is done. –Any part of a force that does not act in the

direction of motion does no work on an object.

Work

• Work depends on direction– If all of the force acts in the same direction as

the motion, all of the force does work.– If part of the applied force acts in the

direction of motion, that part of the force does work.– If none of the force is applied in the direction

of the motion, the force does no work.

Calculating Work

When using SI units in the work formula, the force is in newtons, and distance is in meters.The joule (J) is the SI unit of work. A joule is equal to 1 newton-meter.

Problem

A weight lifter raises a 1600-newton barbell to a height of 2.0 meters.

Power

• Power is the rate at which work is done• Doing work at a faster rate requires more

power. To increase power, you can increase the amount of work done in a given time, or you can do a given amount of work in less time.

Power

• The SI unit for Power is the watt (W) which equals 1 joule per second

Problem

You exert a vertical force of 72 newtons to lift a box to a height of 1.0 meter in a time of 2.0 seconds. How much power is used to lift the box?

Problem

You exert a vertical force of 72 newtons to lift a box to a height of 1.0 meter in a time of 2.0 seconds. How much power is used to lift the box?

Problem

You lift a book from the floor to a bookshelf 1.0 m above the ground. How much power is used if the upward force is 15.0 N and you do the work in 2.0 s?

Problem

You apply a horizontal force of 10.0 N to pull a wheeled suitcase at a constant speed of 0.5 m/s across flat ground. How much power is used? (Hint: The suitcase moves 0.5 m/s. Consider how much work the force does each second and how work is related to power.)

Horsepower

• 1 horsepower = 746 watts• Defined by James Watt – Way to compare power output of steam engines

in 1700s

Work and Machines

• A machine is something that changes a force– Machines make work easier to do• Change size of force needed• Change the direction of the force• Change the distance over which the force acts

• Because of friction work done by a machine (output) is always less than the work done on the machine (input)

Work Input and Work Output

• Input force– Force exerted on a machine (this is done by you)

• Input distance– Distance the input force acts through • Remember W=Fd

• Work input=input force x input distance

Work Input and Work Output

• Output force– Force exerted by a machine (what the machine

does)• Output distance– Distance the output force is exerted through

• Work output– Output force multiplied by the output distance

Problem

What is the output distance of a machine that requires 2 newtons of force exerted over 6 meters and whose output force is 4 newtons?

Mechanical Advantage

• Mechanical advantage of a machine is the number of times that the machine increases an input force

• Due to friction the actual mechanical advantage is always less than the ideal mechanical advantage

Actual Mechanical Advantage (AMA)

• The actual mechanical advantage (AMA) equals the ratio of the output force to the input force.

Ideal Mechanical Advantage (IMA)

• The ideal mechanical advantage (IMA) of a machine is the mechanical advantage in the absence of friction.

Problem

A woman drives her car up onto wheel ramps to perform some repairs. If she drives a distance of 1.8 meters along the ramp to raise the car 0.3 meter, what is the ideal mechanical advantage (IMA) of the wheel ramps?

Problem

A student working in a grocery store after school pushes several grocery carts together along a ramp. The ramp is 3 meters long and rises 0.5 meter. What is the ideal mechanical advantage of the ramp?

Problem

A construction worker moves a crowbar through a distance of 0.50 m to lift a load 0.05 m off of the ground. What is the IMA of the crowbar?

Efficiency

• Efficiency is the percentage of the work input that becomes work output.

• Due to friction…guess what…efficiency is always less than 100%

• Reducing friction increases efficiency

Problem

• If the work input of a machine is 250 J and the work output is 193 J, than what is the total efficiency of the machine?

Energy

• Energy is the ability to do work, therefore work is the transfer of energy– The SI unit for energy is a joule (J)

• The energy of motion is called kinetic energy (KE)

Problem

A 0.10-kilogram bird is flying at a constant speed of 8.0 m/s. What is the bird’s kinetic energy?

Problem

A 50.0-kilogram cheetah has a kinetic energy of 18,000 J. How fast is the cheetah running?

Energy

• Potential Energy (gravitational potential energy) is energy stored as a result of position or shape

Remember g = 9.8 m/s2

Problem

What is the potential energy relative to the water surface of a diver at the top of a 10.0-meter-high diving platform. Suppose she has a mass of 50.0 kilograms.

Elastic Potential Energy

• The potential energy of an object that is stretched or compressed

Forms of energy

• Mechanical energy• Thermal energy• Chemical energy• Electrical energy• Electromagnetic energy• Nuclear energy

Mechanical Energy

• The energy associated with the motion and position of everyday objects is mechanical energy.

• Mechanical energy is the sum of an object’s potential energy and kinetic energy.

Thermal Energy

• The total potential and kinetic energy of all the microscopic particles in an object make up its thermal energy.

• When an object’s atoms move faster, its thermal energy increases, and the object becomes warmer.

Chemical, Electrical, EM, and Nuclear Energy

• Chemical energy is the energy stored in chemical bonds.

• Electrical energy is the energy associated with electric charges.

• Electromagnetic energy is a form of energy that travels through space in the form of waves.

• The energy stored in atomic nuclei is known as nuclear energy– Nuclear Fission – releases energy by splitting an atom– Nuclear Fusion releases energy by combining atoms

Energy Conversion

• Energy can be converted from one form to another

Law of Conservation of Energy• Energy cannot be created nor destroyed, but

only transformed• In a closed system, energy input = energy output– Ex. Falling objects: PE=KE; mgh=1/2mv2

Mechanical Energy

• Mechanical Energy (ME) = KE + PE

Problem

At a construction site, a 1.50-kg brick is dropped from rest and hits the ground at a speed of 26.0 m/s. Assuming air resistance can be ignored, calculate the gravitational potential energy of the brick before it was dropped.

Problem

A 10-kg rock is dropped and hits the ground below at a speed of 60 m/s. Calculate the gravitational potential energy of the rock before it was dropped. You can ignore the effects of friction.

Problem

A diver with a mass of 70.0 kg stands motionless at the top of a 3.0-m-high diving platform. Calculate his potential energy relative to the water surface while standing on the platform, and his speed when he enters the pool. (Hint: Assume the diver’s initial vertical speed after diving is zero.)

Problem

A pendulum with a 1.0-kg weight is set in motion from a position 0.04 m above the lowest point on the path of the weight. What is the kinetic energy of the pendulum at the lowest point? (Hint: Assume there is no friction.)

Energy and Mass

• Einstein’s Theory of Special Relativity– E=mc2

– Energy and mass are equivalent and can be converted into each other

– E is energy, m is mass, and c is the speed of light– c = 3x108 m/s or 176,000 mi/s