The greatest force a level road can exert on the tires of a certain 2000 kg car
ID: 1417110 • Letter: T
Question
The greatest force a level road can exert on the tires of a certain 2000 kg car is 4 kN. What is the highest speed the car can round a curve of radius 200 m without skidding? The greatest force a level road can exert on the tires of a certain 2000 kg car is 4 kN. What is the highest speed the car can round a curve of radius 200 m without skidding? The greatest force a level road can exert on the tires of a certain 2000 kg car is 4 kN. What is the highest speed the car can round a curve of radius 200 m without skidding?Explanation / Answer
The centripetal acceleration a at speed v along a round curve of radius r can be expressed as
a = v^2/r
Multiplying both sides by mass m gives
F = mv^2/r
We can replace mg with F, which is the centripetal force. Solving that for v yields
v = sqrt(Fr/m) = sqrt(4000*200/2000) = 20m/s
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