Question

Bumpers on cars are not of much use in a collision. To see why, calculate the average force a bumper would have to exert if it brought a 1200-kg car (a so-called compact model) to a rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph). (Bumpers are built with springs that compress to provide a stopping force without, hopefully, denting the metal.)

Answer 1

1186.67 N

Step-by-step explanation:

u = Initial velocity = 2 m/s

v = Final velocity = 0

s = Displacement = 0.15 m

a = Acceleration

m = Mass = 1200 kg

Equation of motion

`v^2-u^2=2as\\\Rightarrow a=(v^2-u^2)/(2s)\\\Rightarrow a=(0^2-2^2)/(2* 0.15)\\\Rightarrow a=-13.33\ m/s^2`

Force

`F=ma\\\Rightarrow F=1200* -13.33\\\Rightarrow F=1186.67\ N`

The force that the bumper will exert is 1186.67 N

Answer 2

F = 16 kN

Step-by-step explanation:

given,

mass of the car = 1200 kg

distance travel to stop = 15 cm

initial speed of car = 2 m/s

average force = ?

using equation of motion

v² = u² + 2 as

0² = 2² - 2 a × 0.15 ∵ -ve sign because of deceleration

0.3 a = 4

`a = (4)/(0.3)`

`a = 13.33\ m/s^2`

F = m a

F = 1200 × 13.33

F = 15996 N

F = 16 kN

the average force on the bumper is equal to F = 16 kN