Question

While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If a passenger experiences a force of 226.8 newtons (N) when the car is moving at a speed of 60 kilometers per hour and the passenger has a mass of 70 kilograms, find the force a passenger experiences when the car is moving at 40 kilometers per hour and the passenger has a mass of 90 kilograms

A) 129.6 N
B) 144 N
C) 160 N
D) 115.2N

Answer 1

Answer:

A- 129.6 N

Step-by-step explanation:

Since the centrifugal force on the passenger, F varies jointly as the mass of the passenger, m and the square of the speed of the car,v. In mathematical notation, F ∝ mv² ⇒ F = kmv².

If F₁ = 226.8 Newtons, m₁ = 70 kilograms and speed v₁ = 60 kilometers per hour. From F= kmv², k = F/mv² the proportionality constant. If F₂ is the force on the passenger of mass m₂ = 90 kilograms and speed of car ,v₂ = 40 kilometers per hour. Then,

$k = \frac{F_{1} }{m_{1}v_{1} ^{2} } = \frac{F_{2} }{m_{2}v_{2} ^{2} }\\ F_{2} = F_{1} \frac{m_{2} }{m_{1} }(\frac{v_{2} }{v_{1} }) ^{2} \\F_{2} = 226.8\frac{90 }{70 }(\frac{40 }{60 }) ^{2}\\F_{2} = 129.6 newtons$