Friction force

Static and sliding friction, the support reaction force, the coefficient of friction, the law $F_{\text{fr}} = \mu N$.

Terms

Studied 0 of 5

Formulas

Sliding friction

F_{\text{тр}} = \mu N

Quantities
Symbol	Name	Unit
$F_{\text{тр}}$	magnitude of the sliding friction	N
$\mu$	coefficient of friction	dimensionless
$N$	magnitude of the support reaction force	N

Solved for another quantity:

\mu = \dfrac{F_{\text{тр}}}{N}

N = \dfrac{F_{\text{тр}}}{\mu}

Note. The friction force points against the motion, along the surface. For example, with $\mu = 0.3$ and $N = 20\ \text{N}$ we get $F_{\text{fr}} = 6\ \text{N}$ . Static friction equals the applied force until it exceeds the maximum; in problems this maximum is taken equal to $\mu N$ .

Reaction force of a horizontal support

N = mg

Quantities
Symbol	Name	Unit
$N$	magnitude of the support reaction force	N
$m$	mass of the body	kg
$g$	acceleration of free fall	m/s²

Solved for another quantity:

m = \dfrac{N}{g}

Note. Valid if the body lies on a horizontal surface and there are no other vertical forces (the body is at rest vertically). Then $F_{\text{fr}} = \mu mg$ . Here $g \approx 9.8\ \text{m/s}^2$ ; in problems $10\ \text{m/s}^2$ is often used. For example, $m = 2\ \text{kg}$ , $\mu = 0.3$ : $F_{\text{fr}} = 0.3 \cdot 2 \cdot 10 = 6\ \text{N}$ .

Lab

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

A block on a surface

The block is at rest: the pull does not exceed the maximum static friction.

The vertical forces balance: N = mg. While the block is at rest, the static friction equals the pull and points against it. In motion the friction is μN. The maximum static friction is taken equal to the sliding friction.

Graphs

The red line is the friction force, the grey one is the pull for comparison. Click the graph to set the pulling force.

F_{\text{fr}}(F_{\text{pull}})

N

20 N

F_{\text{fr}}

5 N

a

0 m/s²

Formulas with your numbers

N = mg = 2\cdot 10 = 20\ \text{N}

F_{\text{fr}}^{\max} = \mu N = 0.4\cdot 20 = 8\ \text{N}

F_{\text{fr}} = F = 5\ \text{N}\ \ (F \le 8\ \text{N})

How to read the graphs

While the pull is less than $\mu N$ , the graph $F_{\text{fr}}(F_{\text{pull}})$ follows the line $F_{\text{fr}} = F_{\text{pull}}$ : this is static friction, equal to the pull, and the block stays at rest.
The height of the horizontal part (the plateau) is the maximum static friction, equal to $\mu N$ . Once the pull exceeds it, the block starts to slide.
Once sliding starts, the friction force is constant and does not grow with the pull: $F_{\text{fr}} = \mu N$ . A greater pull gives a greater acceleration, not a greater friction.
Increase $\mu$ or the mass and the plateau rises, because $\mu N = \mu mg$ grows.
The thin line $F_{\text{fr}} = F_{\text{pull}}$ is for comparison: the point where the graph leaves it is the moment sliding begins.

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Terms

Studied 0 of 5

Formulas

Sliding friction

F_{\text{тр}} = \mu N

Quantities
Symbol	Name	Unit
$F_{\text{тр}}$	magnitude of the sliding friction	N
$\mu$	coefficient of friction	dimensionless
$N$	magnitude of the support reaction force	N

Solved for another quantity:

\mu = \dfrac{F_{\text{тр}}}{N}

N = \dfrac{F_{\text{тр}}}{\mu}

Reaction force of a horizontal support

N = mg

Quantities
Symbol	Name	Unit
$N$	magnitude of the support reaction force	N
$m$	mass of the body	kg
$g$	acceleration of free fall	m/s²

Solved for another quantity:

m = \dfrac{N}{g}

Lab

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

A block on a surface

The block is at rest: the pull does not exceed the maximum static friction.

Graphs

The red line is the friction force, the grey one is the pull for comparison. Click the graph to set the pulling force.

F_{\text{fr}}(F_{\text{pull}})

N

20 N

F_{\text{fr}}

5 N

a

0 m/s²

Formulas with your numbers

N = mg = 2\cdot 10 = 20\ \text{N}

F_{\text{fr}}^{\max} = \mu N = 0.4\cdot 20 = 8\ \text{N}

F_{\text{fr}} = F = 5\ \text{N}\ \ (F \le 8\ \text{N})

How to read the graphs

While the pull is less than

\mu N

, the graph

F_{\text{fr}}(F_{\text{pull}})

follows the line

F_{\text{fr}} = F_{\text{pull}}

: this is static friction, equal to the pull, and the block stays at rest.

The height of the horizontal part (the plateau) is the maximum static friction, equal to

\mu N

. Once the pull exceeds it, the block starts to slide.

Once sliding starts, the friction force is constant and does not grow with the pull:

F_{\text{fr}} = \mu N

. A greater pull gives a greater acceleration, not a greater friction.

Increase

\mu

or the mass and the plateau rises, because

\mu N = \mu mg

grows.

The thin line

F_{\text{fr}} = F_{\text{pull}}

is for comparison: the point where the graph leaves it is the moment sliding begins.