Physics

Problem

When several objects move with the same constant speed, their kinetic energies are found to vary linearly with mass. For two of the objects the following data are obtained: Mass

m_1 = 2\,\text{kg}

, Kinetic energy

K_1 = 18\,\text{J}

Mass

m_2 = 5\,\text{kg}

, Kinetic energy

K_2 = 45\,\text{J}

Using this information, answer the questions below. a. (i) Determine the speed common to all the objects. b. (ii) Calculate the kinetic energy of an object of mass

4\,\text{kg}

moving at this speed. c. (iii) If another object moving at the same speed possesses

81\,\text{J}

of kinetic energy, find its mass.

Intuitive explanation

Kinetic energy depends on both mass and speed through the formula $K = \frac{1}{2}mv^2$ . Since all objects move at the same constant speed, kinetic energy scales linearly with mass—the speed is a hidden constant factor. You can find that constant speed using either data point, then use it to predict the kinetic energy of any other object moving at that same speed.

Intuitive explanation

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