The speedometer of a car counts the turns of a wheel and assumes a wheel of radius 30 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The speedometer of a car counts the turns of a wheel and assumes a wheel of radius . New tyres of radius are fitted. When the speedometer shows , what is the real speed? When the distance meter shows , what distance has the car really travelled?
Need a reminder? The key ideaShow
One turn of a wheel rolls , so turns roll . A hand or blade that turns through a fraction of a full turn sweeps that fraction of the area of the circle. Change all lengths to one unit first.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Assumed radius . Real radius .
Plan. The same number of turns is counted in both cases. The meter shows , but the car really moves .
Step 1. The ratio. .
Step 2. The speed. .
Step 3. The distance. .
Answer: the real speed is and the real distance is .
Watch out. The value of and the factor are the same on both sides, so they cancel. Only the ratio of the radii matters.
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