Question

The Kinetic energy, K, of an object with mass m moving with velocity v can be found using the formula - E_{\text{k}}={\tfrac {1}{2}}mv^{2}
. A scientist measured the velocity of a 5-kilogram object and a 20-kilogram object in an experiment. If the velocity of the 5-kilogram object was twice the velocity of the 20-kilogram object, what was the ratio of the kinetic energy of the 5 kilogram object to the kinetic energy of the 20-kilogram object?

Answer 1

Answer:

The ratio of kinetic energies of 5 kg object to 20 kg object is 1:1.

Explanation:

Kinetic energy is defined as energy possessed by an object due to its motion.It is calculated by:

$K.E=\frac{1}{2}mv^2$

Kinetic energy of the 5 kg object.

Mass of object,m = 5 kg

Velocity of an object = v

$K.E=\frac{1}{2}mv^2=\frac{1}{2}\times 5kg\times v^2$

Kinetic energy of the 20 kg object.

Mass of object,m' = 20 kg

Velocity of an object = v'

$K.E=\frac{1}{2}mv^2=\frac{1}{2}\times 20kg\times v'^2$

The ratio of the kinetic energy of the 5 kilogram object to the kinetic energy of the 20-kilogram object:

$\frac{K.E}{K.E'}=\frac{\frac{1}{2}\times 5kg\times v^2}{\frac{1}{2}\times 20kg\times v'^2}$

Given that, v = 2v'

$\frac{K.E}{K.E'}=\frac{1}{1}$

The ratio of kinetic energies of 5 kg object to 20 kg object is 1:1.