PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A typical family car, of mass 1.2×103 kg, driving along a road is subject to two forces that act in the opposite direction to its motion. These two forces are dynamic friction between the tyres and the road and a frictional drag force caused by the car moving through the air.
The frictional drag force, Fd, acting on the car is given by
Fd=21CAρv2 ,
(1) If the coefficient of dynamic friction, μk, is 0.02, calculate the dynamic friction force acting on the moving car. (g=9.81 Nkg−1)
- How does this dynamic friction force change when the car's speed increases?
(2) For a typical family car, C=0.3 and A=2.0 m2. Given that the density of air is 1.3 kgm−3, calculate the speed at which frictional drag force is equal to the dynamic frictional force.
(3) Hence, determine the driving force from the engine necessary to maintain this constant speed.
(4) Most family cars are capable of travelling at 45 ms−1 (in most countries, this speed would be faster than the legal speed limit). With reference to the two frictional forces examined in this question, suggest why typical family cars are not designed to travel at speeds higher than this.
(5) Higher-performance cars and some high-end sports cars are designed to be able to travel at speeds higher than 45 ms−1. Suggest how the design of these cars enables them to travel at such high speeds.