Force. Adding forces. The resultant

Force as a measure of the action of one body on another, measuring force with a dynamometer, the resultant of two forces along one straight line.

Terms

Studied 0 of 3

Formulas

Resultant of forces in the same direction

R = F_1 + F_2

Quantities
Symbol	Name	Unit
$R$	magnitude of the resultant	N
$F_1$	magnitude of the first force	N
$F_2$	magnitude of the second force	N

Solved for another quantity:

F_1 = R - F_2

F_2 = R - F_1

Note. The forces act along one straight line in the same direction. The resultant points in that same direction.

Resultant of forces in opposite directions

R = |F_1 - F_2|

Quantities
Symbol	Name	Unit
$R$	magnitude of the resultant	N
$F_1$	magnitude of the first force	N
$F_2$	magnitude of the second force	N

Solved for another quantity:

F_1 = F_2 + R

F_2 = F_1 - R

Note. The forces act along one straight line in opposite directions. The resultant points the way of the greater force; if $F_1 = F_2$ , then $R = 0$ and the forces are balanced. The expressions for $F_1$ and $F_2$ are written for the case $F_1 > F_2$ .

Lab

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

Two forces acting on a body

The arrow length is proportional to the magnitude of the force: 1 N is the same number of pixels for every arrow.

Graphs

The R(F₂) graph is drawn for the current F₁ and directions. Click the graph to set F₂.

R(F_2)

R

2 N

F_1

4 N, right →

F_2

6 N, ← left

Formulas with your numbers

R = |F_1 - F_2| = |4 - 6| = 2\ \text{N}

How to read the graphs

On the $R(F_2)$ graph for a given force $F_1$ : for forces in the same direction it is the straight line $R = F_1 + F_2$ starting at $R = F_1$ .
For forces in opposite directions the graph is a «check mark» $R = |F_1 - F_2|$ : it falls to zero at $F_2 = F_1$ (the forces balance each other) and then grows.
At $F_2 = 0$ the resultant equals $F_1$ for any directions: the second force has no effect.
The point on the graph is the current value of $F_2$ from the lab; its height equals the length of the resultant arrow in the scene (in the same newtons).

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Terms

Studied 0 of 3

Formulas

Resultant of forces in the same direction

R = F_1 + F_2

Quantities
Symbol	Name	Unit
$R$	magnitude of the resultant	N
$F_1$	magnitude of the first force	N
$F_2$	magnitude of the second force	N

Solved for another quantity:

F_1 = R - F_2

F_2 = R - F_1

Note. The forces act along one straight line in the same direction. The resultant points in that same direction.

Resultant of forces in opposite directions

R = |F_1 - F_2|

Quantities
Symbol	Name	Unit
$R$	magnitude of the resultant	N
$F_1$	magnitude of the first force	N
$F_2$	magnitude of the second force	N

Solved for another quantity:

F_1 = F_2 + R

F_2 = F_1 - R

Lab

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

Two forces acting on a body

The arrow length is proportional to the magnitude of the force: 1 N is the same number of pixels for every arrow.

Graphs

The R(F₂) graph is drawn for the current F₁ and directions. Click the graph to set F₂.

R(F_2)

R

2 N

F_1

4 N, right →

F_2

6 N, ← left

Formulas with your numbers

R = |F_1 - F_2| = |4 - 6| = 2\ \text{N}

How to read the graphs

On the

R(F_2)

graph for a given force

F_1

: for forces in the same direction it is the straight line

R = F_1 + F_2

starting at

R = F_1

For forces in opposite directions the graph is a «check mark»

R = |F_1 - F_2|

: it falls to zero at

F_2 = F_1

(the forces balance each other) and then grows.

F_2 = 0

the resultant equals

F_1

for any directions: the second force has no effect.

The point on the graph is the current value of

F_2

from the lab; its height equals the length of the resultant arrow in the scene (in the same newtons).