Question

During a collision when an average stopping force F is exerted on a car by an obstacle, the car's bumper retracts a distance Δx. These two quantities are related by the equation FΔx=0.5mv0^2.

Use proportional reasoning to determine the necessary percent change in the retraction distance so that the average force required to stop a car is reduced by 26 %.

Express your answer as a percentage. Enter positive value if the distance increases and negative value if the distance decreases.

The percent change = %

Use proportional reasoning to determine the percent change in initial to final speed that would produce the same reduction in force.

Express your answer as a percentage. Enter positive value if the distance increases and negative value if the distance decreases.

The percent change = %

Answer 1

assuming the speed of the ar remains const.

Fx = const. (K)

F and are inversely proportional,

the force is reduced by 26%

new Force F' = F*0.74

F' *x' = K

x' = K/F' = K/F*0.74 = x/0.74 = 1.35x

=> x is increased by +35%

2. Now we assume x remains const , chnage ins speed of the car bring the same reduction of force

F and v² are directly proportional

F = K v² , K is const of proportionality

now F is reduced to F' = 0.74F

0.74F = K v'²  

0.74v² = v'²

v' = 0.86 v

=> 14% reduction in average speed would bring the same reduction in Force