Work and Power Notes.docx

7/29/2019 Work and Power Notes.docx

1/6

Work and Power

Work

To change an objects position, we need to apply a force on the object over the given distance.

This requires work to be done on the object. Work done:

where is the force applied on the object (N) and is the displacement of the object (m) ( and are in the same direction). Work is measured in Nm or joules (1 Nm = 1 J).

Power

Power is the rate which energy is used or given off:

whereEor Ware in J and tis in s. Power is measured in Watts (W) or J/s (1 W = 1 J/s).

Example 1

A cross country skier of mass 85 kg travels 600 m along the snowy trail which has a coefficient

of friction of 0.10. He does this trip in 3.0 min.

a) Determine his work done.

*Assume is applied over 600 m.

b) Determine his power output.

Mechanical Energy

We can derive each of these energy equations from the work equation , where d isparallel toF.


2/6

Types of Energy

Gravitational Potential Energy, The work needed to be done to lift the box of

mass m from a height hito a new height hfis

( )

*We assume weight mg is constant from hito hf-

this is OK as long as we dont go too high.

Since work changes the potential energy of the

box,

Thus we have shown that the potential energy of

h = 0 reference ( )


3/6

a mass m at a height h above the reference is measured in Joules (J) (assumeconstant g = 9.8 N/kg).

Kinetic Energy,

Work done on an object can change its speed and consequently its kinetic energy.

Thus we have shown that the kinetic energy of an object due to its motion is Elastic Potential Energy,

When we stretch a spring, it has the potential spring back. So the force we apply on the spring

changes its elastic potential energy.

The force we apply on a spring to extend it depends on how much we extend it by:

d

mm

F


4/6

Conservation of (Mechanical) Energy

When mechanical energy is conserved, the sum of the and at one instant is equal to thesum of the and at a different instant (there is no energy transformed to heator sound).

Question

Justin, who has a mass of 72.7 kg, rides the roller coaster. He moves at 1.0 m/s as he goes past

point A. Assuming africtionless track, calculate the speed of Justin as he goes through point B

and point C on his exhilarating trip.


5/6

a) Point B: Mechanical Energy at A = Mechanical Energy at B

b) Point C: Mechanical Energy at A = Mechanical Energy at C

Note: We can find the speed at point C by considering the conditions at B instead of A.

Machines and Efficiency

The efficiency of a machine is determined by

For machines, WOutput changes the mechanical energy of the object.

The Pulley as a Simple Machine

Machine


6/6

Mechanical Advantage, MA

Ideal Mechanical Advantage, IMA

Due to friction in the pulley, for one pulley only so

Documents

Work and Power Notes.docx