Question #660d8

Question

Question #660d8

1 Answer

Impact of this question

1523 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-28T23:35:11

$7.35 c m^{2}$ $7.35 cm^2$

Explanation:

The equation for pressure is:
$p = \frac{F}{A}$ $p=F/A$

The force responsible for providing the pressure in the tyres is the weight of the bicycle plus rider.
$w = m g = 90.0 \times 9.8 = 882 N$ $w = mg = 90.0 × 9.8 = 882 N$

But the weight is distributed across two tyres equally (we assume this). So the actual force involved is:
$F = \frac{w}{2} = \frac{882}{2} = 441 N$ $F=w/2 = 882/2=441N$

Now rearrange the pressure equation to solve for the contact area:
$A = \frac{F}{p} = \frac{w / 2}{p} = \frac{441}{600 \times 10^{3}} = 0.000735 m^{2}$ $A = F/p=(w//2)/p=441/(600×10^3)=0.000735 m^2$

The area is small so it might be more convenient to use a prefix, i.e. $c m^{2}$ $cm^2$ :
$A = 0.000735 \times {(10^{2})}^{2} = 7.35 c m^{2}$ $A=0.000735 × (10^2)^2 = 7.35 cm^2$

That is a reasonable value for the area of bicycle tyres in contact with the ground.

When converting areas into a prefix the conversion factor must be squared that's why I multiplied by ${(10^{2})}^{2}$ $(10^2)^2$ above. The $10^{2}$ $10^2$ is the conversion factor for centi.
Find out more about prefix conversions here:

Science

Math

Humanities

... and beyond

Question #660d8

1 Answer

Explanation:

Related questions

Impact of this question