Mechanical work and power

Mechanical work when the force acts along the displacement, the joule, power, the watt, the link between power, force and speed.

Terms

Studied 0 of 4

Formulas

Mechanical work

A = F s

Quantities
Symbol	Name	Unit
$A$	mechanical work	J
$F$	force acting along the displacement	N
$s$	distance travelled	m

Solved for another quantity:

F = \dfrac{A}{s}

s = \dfrac{A}{F}

Note. The formula holds when the force is directed along the displacement. For example, a cart is pulled with a force of $50\ \text{N}$ over $4\ \text{m}$ : $A = 50\cdot 4 = 200\ \text{J}$ .

Power

N = \dfrac{A}{t}

Quantities
Symbol	Name	Unit
$N$	power	W
$A$	work	J
$t$	time in which the work was done	s

Solved for another quantity:

A = N t

t = \dfrac{A}{N}

Note. For example, work of $200\ \text{J}$ is done in $10\ \text{s}$ : $N = 200 / 10 = 20\ \text{W}$ .

Power from force and speed

N = F v

Quantities
Symbol	Name	Unit
$N$	power	W
$F$	force acting along the motion	N
$v$	speed of the uniform motion	m/s

Solved for another quantity:

F = \dfrac{N}{v}

v = \dfrac{N}{F}

Note. Follows from $N = A / t = F s / t$ and $v = s / t$ for uniform motion. For example, a force of $100\ \text{N}$ at $3\ \text{m/s}$ : $N = 300\ \text{W}$ .

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

A cart is pulled along a table

The force is directed along the displacement and the cart moves uniformly. Friction is not considered: only the work of the pulling force is counted.

Distance travelled4 m

Graphs

A(s)

The slope of the line is the force F

A

200 J

N

20 W

v

0.4 m/s

A(4\ \text{m})

200 J

Formulas with your numbers

A = F s = 50\cdot 4 = 200\ \text{J}

N = \dfrac{A}{t} = \dfrac{200}{10} = 20\ \text{W}

N = F v = 50\cdot 0.4 = 20\ \text{W}

How to read the graphs

The $A(s)$ graph is a straight line through the origin: work is directly proportional to the distance, $A = F s$ .
The slope of the graph is the force: the greater the force $F$ , the steeper the line. From the graph the force is $F = A / s$ .
Work does not depend on time: pulling with the same force over the same distance more slowly gives the same work but a smaller power.
If the distance $s = 0$ (the body did not move) or the force $F = 0$ , the mechanical work is zero.

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Terms

Studied 0 of 4

Formulas

Mechanical work

A = F s

Quantities
Symbol	Name	Unit
$A$	mechanical work	J
$F$	force acting along the displacement	N
$s$	distance travelled	m

Solved for another quantity:

F = \dfrac{A}{s}

s = \dfrac{A}{F}

Note. The formula holds when the force is directed along the displacement. For example, a cart is pulled with a force of $50\ \text{N}$ over $4\ \text{m}$ : $A = 50\cdot 4 = 200\ \text{J}$ .

Power

N = \dfrac{A}{t}

Quantities
Symbol	Name	Unit
$N$	power	W
$A$	work	J
$t$	time in which the work was done	s

Solved for another quantity:

A = N t

t = \dfrac{A}{N}

Note. For example, work of $200\ \text{J}$ is done in $10\ \text{s}$ : $N = 200 / 10 = 20\ \text{W}$ .

Power from force and speed

N = F v

Quantities
Symbol	Name	Unit
$N$	power	W
$F$	force acting along the motion	N
$v$	speed of the uniform motion	m/s

Solved for another quantity:

F = \dfrac{N}{v}

v = \dfrac{N}{F}

Note. Follows from $N = A / t = F s / t$ and $v = s / t$ for uniform motion. For example, a force of $100\ \text{N}$ at $3\ \text{m/s}$ : $N = 300\ \text{W}$ .

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

A cart is pulled along a table

The force is directed along the displacement and the cart moves uniformly. Friction is not considered: only the work of the pulling force is counted.

Distance travelled4 m

Graphs

A(s)

The slope of the line is the force F

A

200 J

N

20 W

v

0.4 m/s

A(4\ \text{m})

200 J

Formulas with your numbers

A = F s = 50\cdot 4 = 200\ \text{J}

N = \dfrac{A}{t} = \dfrac{200}{10} = 20\ \text{W}

N = F v = 50\cdot 0.4 = 20\ \text{W}

How to read the graphs

The

A(s)

graph is a straight line through the origin: work is directly proportional to the distance,

A = F s

The slope of the graph is the force: the greater the force

F

, the steeper the line. From the graph the force is

F = A / s

Work does not depend on time: pulling with the same force over the same distance more slowly gives the same work but a smaller power.

If the distance

s = 0

(the body did not move) or the force

F = 0

, the mechanical work is zero.