Question

Mathematically, explain how a car (A) with mass of 500 kg and velocity of 2 m/s has the same kinetic energy as a car (B) with mass of 20000 g and velocity of 10 m/s.

Answer 1

Answer:

Both kinetic energies are equal

Explanation:

Kinetic Energy

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

The equation for the kinetic energy is:

$\displaystyle K=\frac{1}{2}mv^2$

Where:

m = mass of the object

v = speed of the object

The kinetic energy is expressed in Joules (J)

There are two cars:

Car (A) with mass ma=500 kg and speed va= 2 m/s

Car (B) with mass mb=20,000 gr and speed vb= 10 m/s

Calculate the kinetic energy of both cars:

$\displaystyle K_a=\frac{1}{2}m_av_a^2$

$\displaystyle K_a=\frac{1}{2}500*2^2$

$\displaystyle K_a=250*4=1,000 J$

To calculate the Kb, the mass must be expressed in kg:

mb=20,000/1,000 =20 Kg

$\displaystyle K_b=\frac{1}{2}m_bv_b^2$

$\displaystyle K_b=\frac{1}{2}20*10^2$

$\displaystyle K_b=10*100=1,000 J$

Both kinetic energies are equal