Question

Two cars are driving at the same velocity, but one has twice the mass of the other. Is the mechanical kinetic energy of the larger car two times, three times, or four times that of the smaller car

Answer 1

Kinetic energy is dependent on the square of the velocity and directly proportional to mass. Thus, if two cars have the same velocity but different masses, the car with twice the mass will have twice the kinetic energy.

Step-by-step explanation:

If two cars are driving at the same velocity, but one has twice the mass of the other, the kinetic energy of the larger car is not directly proportional to its mass. Instead, kinetic energy (KE) is calculated using the formula KE = (1/2)mv2, where ‘m’ represents mass and ‘v’ represents velocity. This means that the kinetic energy depends on the square of the velocity and is directly proportional to the mass. Therefore, if one car has twice the mass of the other but both have the same velocity, the car with the larger mass will have twice the kinetic energy of the smaller one.

Answer 2

The kinetic energy of the larger car is two times that of the smaller car

Step-by-step explanation:

Kinetic Energy

Is the energy an object has due to its state of motion. It's proportional to the square of the speed.

The equation for the kinetic energy is:

`\displaystyle K=(1)/(2)mv^2`

Where:

m = mass of the object

v = speed at which the object moves

The kinetic energy is expressed in Joules (J)

It's required to compare the kinetic energy of two cars K1 and K2. Car 2 has twice the mass of car 1: m2=2m1, and they have the same speed.

The kinetic energy of car 1 is:

`\displaystyle K_1=(1)/(2)m_1v^2`

The kinetic energy of car 2 is:

`\displaystyle K_2=(1)/(2)m_2v^2`

Substituting the relation of the masses:

`\displaystyle K_2=(1)/(2)(2m_1)v^2`

Rearranging:

`\displaystyle K_2=2\left((1)/(2)m_1v^2\right)`

Substituting the kinetic energy of car 1:

`\displaystyle K_2=2K_1`

The kinetic energy of the larger car is two times that of the smaller car