An automobile that has a mass of 1.3 x 103 Kg, has 3.9 x 105 J of kinetic energy when it has speed of 24.6 m s-1 (88.6 km h-1). What height should you lift the car to have this energy?

energy = m g h

3.9E5 = 1.3E3 * g * h

Hi Sammie! Which school are you in?

To calculate the height at which you should lift the car in order to have a specific kinetic energy, we will use the principle of conservation of energy.

The total mechanical energy of the car at any point can be given as the sum of its kinetic energy and potential energy. Mathematically, this can be expressed as:

E = KE + PE

Where:
E = total mechanical energy (constant)
KE = kinetic energy
PE = potential energy

In this case, we know the kinetic energy (KE) of the car is 3.9 x 10^5 J, and we need to find the potential energy (PE) when the car is lifted to a certain height.

Since the car is not moving vertically, we can assume that the total mechanical energy (E) remains constant throughout the motion (ignoring any energy losses due to friction or air resistance). Therefore, we can equate the initial kinetic energy with the final potential energy when the car is lifted:

KE_initial = PE_final

Now we can calculate the potential energy (PE) using the formula:

PE = mgh

Where:
m = mass of the car (1.3 x 10^3 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height

Substituting the known values into the equation, we have:

3.9 x 10^5 J = (1.3 x 10^3 kg) * (9.8 m/s^2) * h

Simplifying the equation:

h = (3.9 x 10^5 J) / [(1.3 x 10^3 kg) * (9.8 m/s^2)]

h = (3.9 x 10^5 J) / (1.274 x 10^4 kg*m/s^2)

h ≈ 30.56 meters

Therefore, you would need to lift the car to a height of approximately 30.56 meters to have the same kinetic energy as given in the question.