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

A- 129.6 N

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 = (F_(1) )/(m_(1)v_(1) ^(2) ) = (F_(2) )/(m_(2)v_(2) ^(2) )\\ F_(2) = F_(1) (m_(2) )/(m_(1) )((v_(2) )/(v_(1) )) ^(2) \\F_(2) = 226.8(90 )/(70 )((40 )/(60 )) ^(2)\\F_(2) = 129.6 newtons`