WORK A force that causes a displacement of

WORK • A force that causes a displacement of an object does work on the object. W=Fd • 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 mv 2 • 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 x 2 – 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 mv 2 = mgh • PEi + KEi = PEf + KEf • (mgh)1 + (½ mv 2)1 = (mgh)2 + ( ½mv 2)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 t P = F d_ 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 k. W, 3. 5 k. W, and 5. 5 k. W. Which motor is best for the job?