Question

determine the ratio of the kinetic energies of the two bodies A and B of equal mass but the velocity of A being half of that of B

Answer 1

Answer:

Well, let’s plug in the variables in the Kinetic Energy equation; K.E=1/2mv^2, and we will make m=3 and v=8 for the first body of mass, and for the second, m=3 and v=4. I will put a 1 and a 2 beside the K.E to signify which body of mass I am calculating. K.E1=1/2(3)(8^2), =1/2(3)(64), =1/2(192), K.E1=96 Joules of Energy. Now for the second object of mass. K.E2=1/2(3)(4^2), =1/2(3)(16), =1/2(48), =1/2(144), K.E2=24 Joules of Energy. As you can see the second body of mass, with the same mass as the first one but with half of the velocity, has 1/4 the Kinetic Energy of the 1st body of mass.

Answer 2

Answer:

The ratio of the kinetic energies of A and B will be 1/4.

Explanation:

Let the mass of A and B be m Kg and let the velocity of A be V m/s.

As given in the question velocity of A is half of that of B.

so, the velocity of B = 2 ˣ velocity of A

                                 = 2V m/s

the kinetic energy of any body = $\frac{1}{2} mv^2$

Then, the ratio of the kinetic energies of the bodies A and B will be

$\frac{K.E ofA}{K.E of B} =\frac{\frac{1}{2}mv^2 }{\frac{1}{2} m4v^2}$

$\frac{K.E of A}{K.E of B } = \frac{1}{4}$

hence, the ratio of the kinetic energies of A and B is 1/4.