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

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

Step-by-step explanation:

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

`K.E=(1)/(2)mv^2`

Kinetic energy of the 5 kg object.

Mass of object,m = 5 kg

Velocity of an object = v

`K.E=(1)/(2)mv^2=(1)/(2)* 5kg* v^2`

Kinetic energy of the 20 kg object.

Mass of object,m' = 20 kg

Velocity of an object = v'

`K.E=(1)/(2)mv^2=(1)/(2)* 20kg* v'^2`

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

`(K.E)/(K.E')=((1)/(2)* 5kg* v^2)/((1)/(2)* 20kg* v'^2)`

Given that, v = 2v'

`(K.E)/(K.E')=(1)/(1)`

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