Question

Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs. Find the kinetic energy for a mass of 4 grams and a velocity of 6 centimeters per second.

Answer 1

72 ergs

Step-by-step explanation

Step 1

Kinetic energy varies jointly as the mass and the square of the velocity,then

`E_k=\lambda\cdot m\cdot v^2`

where

m is the mass, v is the velocity and

`\lambda\text{ is a constant}`

A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs

`\begin{gathered} E_k=\lambda m\cdot v^2 \\ 36\text{ erg=}\lambda\cdot8\cdot3^2 \\ 36=\lambda\cdot8\cdot9 \\ 36=\lambda\cdot72 \\ \text{divide both sides by 72} \\ (36)/(72)=\lambda \\ \lambda=(1)/(2) \end{gathered}`

so, the equation is

`\begin{gathered} E_k=\lambda\cdot m\cdot v^2 \\ E_k=(1)/(2)\cdot m\cdot v^2 \end{gathered}`

Step 2

now , we know the equation to find the kinetic energy of a object if we know its mass and its velocity

Let

mass= 4 grams

velocity = 6 cms per sec

then

I hope this helps you