WORK

• A force that causes a displacement of an object does work on the object.

W = F d • Work is done

– if the object the work is done on moves due to the force applied.

– only when components of a force are parallel to a displacement.

Work Done by a Force at an Angle

• Resolve the force vector into x and y components.

• The component perpendicular to the displacement does no work.

• Only the component in the direction of movement does work.

W = F d (cos )

Force Without Work being Done

• Carry a bag of groceries while walking along a sidewalk.– The work being done against gravity is

perpendicular to the direction of bag movement.

– The bag is not being moved upward. FA = Fg

– At 90° to the direction of motion the cos 90° = 0; therefore, work = 0.

Work (cont.)

• SI Unit : Joule (J) = 1 N•m

• Scalar quantity – Positive when work is done in the direction

of displacement.– Negative when work is done in the

opposite direction of displacement.

Kinetic Energy

• The energy of an object due to its motion.

KE = ½ mv2

• If 2 objects are traveling with the same speed, the object with the greater mass has more kinetic energy.

Kinetic Energy (cont.)

• SI Unit : Joule– same SI unit as work because it’s directly

related.

• Scalar quantity– If net work is positive, KE increases.– If net work is negative, KE decreases.– If net work done is zero, KE is constant.

Potential Energy

• The energy associated with an object due to its position.

• 2 types of potential energy:

– Gravitational Potential energy

– Elastic Potential energy

Gravitational Potential Energy

• Potential energy associated with the object’s position relative to a gravitational source.

PEg = m g h – A brick held high in the air has the potential

to do work as it falls to earth. W = Fd– Work must be done to lift the brick back

into the air. F = mg; therefore W = mgh =

PEg

Elastic Potential Energy

• The potential energy in a stretched or compressed elastic object such as a spring.

PEelastic = ½ k x2

– Force is needed to compress or stretch the spring. Work is done.

• k = spring constant

• SI Unit for spring constant: N/m

Total Mechanical Energy

• The sum of kinetic energy and all forms of potential energy (gravitational and elastic).– This value remains constant for an object

or system of objects.

– Ex: As a rock falls, the PE decreases and KE increases.

ME = KE + PE

Non-mechanical Energy

• All energy that is not mechanical.– Other forms of energy that are not

significantly involved in motion.– Chemical and electrical energy, heat, light,

and sound.

The Law of Conservation of Energy

• Energy cannot be created nor destroyed, it simply changes form.

• KE = PE

• ½ mv2 = mgh

• PEi + KEi = PEf + KEf

• (mgh)1 + (½ mv2)1 = (mgh)2 + ( ½mv2)2

In the Presence of Friction

• Mechanical energy is not conserved.

• Some energy is lost in the form of heat.

Work-Kinetic Energy Theorem

• The net work done on an object is equal to the change in the kinetic energy of the object.

• Wnet = KEf - KEi

Power

• The time rate of energy transfer.

P = W P = F d_t t

• SI Unit : Watt (W) = 1 J/s

• Large amounts of work – measured in Horsepower

1 HP = 746 W

Sample Problem 1

• How much work is done on a vacuum cleaner pulled 3 m by a force of 50 N at an angle of 30° above the horizontal?

Sample Problem 2

• A 7 kg bowling ball moves at 3 m/s. How much kinetic energy does the bowling ball have?

Sample Problem 3

• A 40 kg child is in a swing that is attached to ropes 2 m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position when the ropes are horizontal.

Sample Problem 4

• The force constant of a spring in a child’s toy car is 550 N/m. How much elastic potential energy is stored in the spring if the spring is compressed a distance of 1.2 cm?

Sample Problem 5

• A 193 kg curtain needs to be raised 7.5 m in as close to 5 s as possible. Three motors are available. The power ratings for the three motors are listed as 1 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job?