Question

2 cars drive at the same velocity but one of them has twice the mass as the other. Is the mechanical kinetic energy of the larger car 2, 3 , or 4 times that of the smaller car? Please include formula and clear explanation.

Answer 1

Step-by-step explanation:

`m1 = x \: \: m2 = 2x`

since they are velocities are the same,

`v1 = v2 = v`

since the two cars are moving they do not possess potential energy so hence the mechanical energy would be equal to the kinetic energy

kinetic energy of the car with the smaller mass.

`k.e = (1)/(2) m {v}^(2) \\ k.e = (1)/(2) x {v}^(2) ...........(1)`

kinetic energy of the larger mass.

`k.e = (1)/(2) m {v}^(2) \\ k.e = (1)/(2) (2x) {v}^(2) \\ k.e = x {v}^(2) ............(2)`

when comparing equation 1 and equation 2 you would see that equation 2 is 2 times as equal as equation 1.

therefore the mechanical energy of the car with the larger mass is two times the kinetic energy of the car with the smaller mass.

Answer 2

The mechanical kinetic energy of the larger car is 4 times that of the smaller car.

Step-by-step explanation:

The mechanical kinetic energy of the larger car is 4 times that of the smaller car.

The formula for kinetic energy is KE = 1/2mv², where m is the mass of the object and v is its velocity.

Since both cars are moving at the same velocity, their kinetic energies are directly proportional to their masses.

Therefore, if one car has twice the mass of the other (m1 = 2m2), the kinetic energy of the larger car (KE1) will be 4 times that of the smaller car (KE2). KE1/KE2 = (1/2)mv²1 / (1/2)mv²2 = (m1/m2)(v²1/v²2) = (2m2/m2)(v²/v²) = 2v²/v² = 4.