Question

Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 12 grams and velocity of 3 centimeters per second has a kinetic energy of 54 ergs. Find the kinetic energy for a mass of 2 grams and velocity of 6 centimeters per second.

Answer 1

36 ergs

Explanation:

KE = k(mv²)

54 = k(12×3²)

k = 54/108 = ½

KE = ½mv²

KE = ½ × 2 × 6² = 36

Answer 2

36 ergs

Explanation:

Joint variation is:

If z varies jointly to x and y, then we have the expression: z = kxy, where k is a constant.

In this case, z is kinetic energy (KE), x is mass (m), and y is the square of the velocity (
`v^2`). So:

KE =
`kmv^2`

We have some values we can plug in to solve for k:

54 = k * 12 *
`3^2`

k = 1/2

Now, we have:

`KE=(1)/(2) mv^2`

To find the kinetic energy for m = 2 and v = 6, we have:

KE =
`(1)/(2) *2*6^2=36`

Thus, the kinetic energy is 36 ergs.

Hope this helps!