Question

An automotive research facility is testing a new design on bumpers to determine the force at which it will break. The formula for Force is F = 1 2 m v 2 Where m is the mass (weight) and v is the velocity (speed)What is the effect on the force if the velocity changes from 5 miles per hour to 10 miles per hour?

Answer 1

Answer: The force increases by 4 units when velocity changes from 5 miles per hour to 10 miles per hour.

Explanation: The force is given by the formula:

`F=(1)/(2)mv^2`

Force when v = 5 miles per hour

`F_1=(1)/(2)m(5)^2`

Force when v = 10 miles per hour

`F_2=(1)/(2)m(10)^2`

Taking ratio of
`F_2` and
`F_1`

`(F_2)/(F_1)=(\left((1)/(2)m(10)^2\right))/(\left((1)/(2)m(5)^2\right))`

`F_2=4F_1`

Hence, the force is increased by 4 units when velocity changes from 5 miles per hour to 10 miles per hour.

Answer 2

The equation that would allow us to calculate for the force is expressed as,

F = 0.5mv²

If we are to evaluate the use of 5 miles per hour then, the equation would be,

F = 0.5m(5 m/s)² = 12.5m

For the second given speed,
F = 0.5m₁(10 m/s)² = 50m

The fraction between the forces is equal 4.