Check out some similar questions!

heyyalliee · Nov 17, 2010, 10:55 AM

To prevent damage to floors (and to increase friction), a crutch will often have a rubber tip attached to its end.
If the end of the crutch is a circle of radius 1.3cm without the tip, and the tip is a circle of radius 2.3cm, by what factor does the tip reduce the pressure exerted by the crutch?

How do I go about doing this problem. I know P=F/A
A=Pi(r)^2
So I can find both Areas. But what do I do after that? Also Should I change the radius to meters instead of cm?

Thanks:)

Unknown008 · Nov 17, 2010, 12:09 PM

The same force is applied on the crutch and the tip. So, you can find the pressure in terms of the force applied, let's say force F.

In this case, you can leave the units in centimetres since the ratio between the two pressures you are looking for will cancel out the units.

heyyalliee · Nov 17, 2010, 12:42 PM

How do I know the force applied? Gravity?

Unknown008 · Nov 17, 2010, 12:51 PM

We don't know the force applied, but since the ratio cancels out the force as well, we don't need to worry about it!

$\text{Pressure on crutch} = \frac{\text{Force on crutch}}{\text{Area of crutch}}$

$P_1 = \frac{F}{A_1}$

$\text{Pressure on tip} = \frac{\text{Force on tip}}{\text{Area of crutch}}$

$P_2 = \frac{F}{A_2}$

Ratio: $\frac{P_1}{P_2} = \frac{ \frac{F}{A_1}}{ \frac{F}{A_2}} = ?$

Can you complete it? :)

heyyalliee · Nov 18, 2010, 08:18 AM

haha maybe. So the F cancels and I have A1/A2.
Above formulas indicate that both A's are areas of crutch. Area of Crutch is Pi(1.3cm)^2. Which I get to be 5.31. So 5.31/ 5.31 is 1, but its saying that's not the right answer.

heyyalliee · Nov 18, 2010, 08:20 AM

oh oh,I got it. I took the Area of the tip and divided by area of the crutch( circle) and got 3.1!
Pi(2.3)^2/Pi(1.3)^2
Thanks for your help!

Unknown008 · Nov 18, 2010, 08:22 AM

Yes, that's it (^^,)b