Mechanical Work and Power:Learning GoalThe student will use appropriate terminology

related to energy including work, gravitational potential energy, kinetic energy, and power; and perform calculations related to the work done in a mechanical system.

Mechanical Work and Power

SPH4C

Mechanical Work: a Definition

The mechanical work on an object is the amount of mechanical energy transferred to that object by a force.

Mechanical Work: a Definition

The mechanical work on an object is the amount of mechanical energy transferred to that object by a force.

W E= ∆

Mechanical Energy: a definition

The mechanical energy of an object is that part of its total energy which is subject to change by mechanical work.

(definition by the Department of Redundancy Department)

Mechanical Energy: a definition

The mechanical energy of an object is that part of its total energy which is subject to change by mechanical work.

(definition by the Department of Redundancy Department)

Energy is a concept so fundamental in physics that it is not easily defined in terms of anything more fundamental.

Mechanical Energy: a definition

The mechanical energy of an object is that part of its total energy which is subject to change by mechanical work.

(definition by the Department of Redundancy Department)

It is easier just to understand energy in terms of its component kinetic and potential energies.

Mechanical Energy: a definition

Kinetic energy is the energy of motion and potential energy is the energy to, potentially, do something else.

Energy: example

Thermal energy, the energy of the particles of a substance, is partly kinetic energy and partly potential energy:

Energy: example

Thermal energy, the energy of the particles of a substance, is partly kinetic energy and partly potential energy:

The kinetic energy is in the kinetic energy of the atoms.

Energy: example

Thermal energy, the energy of the particles of a substance, is partly kinetic energy and partly potential energy:

The kinetic energy is in the kinetic energy of the atoms.

The potential energy is stored in the deformation of atomic bonds during this motion.

Energy: Units

The SI derived unit of work is the Joule:

Energy: Units

The SI derived unit of work is the Joule:

1 12

2Jk g m

s= ⋅

Energy: more units

But there exist other metric units, e.g.

1 3 6 1 0 6k W h J= ×.

Energy: more units

But there exist other metric units, e.g.

1 3 6 1 0 6k W h J= ×.

1 4 1 8 4c a l J= .

Calories

A calorie is the amount of heat necessary to raise the temperature of 1 g of water by 1oC (at standard atmospheric pressure).

Calories

A calorie is the amount of heat necessary to raise the temperature of 1 g of water by 1oC (at standard atmospheric pressure).

Food energy is measured in kilocalories

(or Calories with a capital C).

1 1 1 0 4 1 8 4 1 03 3C a l c a l J= × = ×.

Back to Work

In the simplest case of an object moving in one direction and a constant force applied parallel to that direction:

Back to Work

In the simplest case of an object moving in one direction and a constant force applied parallel to that direction:

Where F is the magnitude of the applied force and ∆d is the distance the object travels. Note that work is a scalar quantity.

W F d= ∆

Work: example 1

Ms. Rosebery applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a frictionless surface. Find the work done on the box.

Work: example 1

Ms. Rosebery applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a frictionless surface. Find the work done on the box.

W

F N

d m

==

=

?

.

.

4 0 0

1 5 0∆

Work: example 1

Ms. Rosebery applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a frictionless surface. Find the work done on the box.

W

F N

d m

==

=

?

.

.

4 0 0

1 5 0∆

W F d

W N m

==

∆( . ) ( . )4 0 0 1 5 0

Work: example 1

Ms. Rosebery applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a frictionless surface. Find the work done on the box.

W

F N

d m

==

=

?

.

.

4 0 0

1 5 0∆

W F d

W N m

W J

==

= ×

∆( . ) ( . )

.

4 0 0 1 5 0

6 0 0 1 0 2

Work: example 2

Ms. Rosebery applies a vertical force of magnitude 40.0 N on a 10.0 kg box as it slides 15.0 m across a frictionless surface. Find the work done on the box.

Work: example 2

Ms. Rosebery applies a vertical force of magnitude 40.0 N on a 10.0 kg box as it slides 15.0 m across a frictionless surface. Find the work done on the box.

W = 0

Work: example 2

Ms. Rosebery applies a vertical force of magnitude 40.0 N on a 10.0 kg box as it slides 15.0 m across a frictionless surface. Find the work done on the box.

Ms. Rosebery is not increasing the speed of the box and thus its mechanical energy. Forces applied at right angles to the motion don’t count.

W = 0

Work done by friction

If there is a frictional force, it will do negative work on the object, i.e. reduce its total mechanical energy.

Work: Example 3

Ms. Rosebery applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a surface. The frictional force is 10.0 N. Find the work done by friction on the box.

Work: Example 3

Ms. Rosebery applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a surface. The frictional force is 10.0 N. Find the work done by friction on the box.

JW

mNW

dFW

21050.1

)0.15)(0.10(

×−=−=∆=

Remember that friction is opposite the direction of motion.

Work: Example 3

The total change in energy of the box would be:

The work done by friction would have gone into creating heat and sound energy.

JE

JJE

WWE frictionRosebery

2

22

1050.4

1050.11000.6

×=∆×−×=∆

+=∆

Power

Power is the rate at which work is performed or energy is transferred:

PW

t=

∆

Power

Power is the rate at which work is performed or energy is transferred:

It has units of J/s or Watts (W).

PW

t=

∆

Power

Power is the rate at which work is performed or energy is transferred:

It has units of J/s or Watts (W).

PW

t=

∆

More Practice

Mechanical Work and Power Lab Activity