Question

Calculate the kinetic energy (in ft-lbf) of a 2,688 lbm car that is traveling at a speed of 68 miles/hr. (The answer should have 6 significant figures.)

Answer 1

To solve this problem we will apply the concept given in Newton's second law for which we will obtain the mass of the body and thus we can obtain the required value to apply it on the definition of kinetic energy.

We know that 'lbm' represents the mass that weighs one pound-force (lbf) on earth. Using Newton's second law

`F = mg`

`m = (F)/(g)`

Here,

F = Force

m = mass

g = Gravitational acceleration

Replacing,

`m = (2688)/(32.174)`

`m = 83.54lbf`

The velocity in feet per second is

`v = 68miles/h ((5280ft)/(1 miles))((1h)/(3600s))`

`v = 99.73ft/s`

Recall that the kinetic energy is half the product between mass and squared velocity, therefore,

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

Here,

m = mass

v = Velocity

Replacing,

`KE = (1)/(2) (83.54)(99.73)`

`KE= 8331.4ft\cdot lbf`

Therefore the kinetic energy is
`8331.4ft\cdot lbf`