Question

Resistance to the motion of an automobile consists of road friction, which is almost independent of speed, and air drag, which is proportional to speed-squared. For a certain car with a weight of 12000 N, the total resistant force F is given by F = 300 + 1.8v2, with F in newtons and v in meters per second. Calculate the power (in horsepower) required to accelerate the car at 0.96 m/s^2 when the speed is 82 km/h.

Answer 1

Answer:

73.52983 Hp

Explanation:

m = Mass of car = $\dfrac{W}{g}$

W = Weight of car = 12000 N

a = Acceleration = 0.96 m/s²

Velocity of the car

$v=82\times \dfrac{1000}{3600}\\\Rightarrow v=\dfrac{82}{3.6}\\\Rightarrow v=\dfrac{41}{1.8}$

From the question

$F=300+1.8v^2\\\Rightarrow F=300+1.8\times \left(\dfrac{41}{1.8}\right)^2\\\Rightarrow F=1233.88\ N$

Balancing the forces

$\dfrac{P}{v}-1233.88=ma\\\Rightarrow P=(ma+12000)v\\\Rightarrow P=\left(\dfrac{12000}{9.81}\times 0.96+1233.88\right)\dfrac{41}{1.8}\\\Rightarrow P=54853.26055\ W=\dfrac{54853.26055}{746}\\\Rightarrow P=73.52983\ Hp$

The power is 73.52983 Hp