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Chapter 3: Problem 34

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 velocity of 6 centimeters per second.

Short Answer

Expert verified
The kinetic energy for a mass of 4 grams and velocity of 6 centimeters per second is 72 ergs.

Step by step solution

01

Identify the variation type and formula

Here, the kinetic energy (K) varies jointly with the mass (m) and the square of velocity (v^2). This sets up the equation \(K = k * m * v^2\), where k is the constant of variation.
02

Find the constant of variation

Use the given values to find the constant. They are mass m = 8 grams, velocity v = 3 cm/s and kinetic energy K = 36 ergs. Plugging these into equation, we get \(36 = k * 8 * 3^2\). Solving this gives, \(k = 0.5\).
03

Find the kinetic energy for new values

Now we know the constant of variation (k), we can find the kinetic energy for mass m = 4 grams and velocity v = 6 cm/s. Substituting the given values, \(K = 0.5 * 4 * 6^2\) gives kinetic energy K = 72 ergs.

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