Question

A shooting star is a meteoroid that burns up when it reaches Earth's atmosphere. Many of these meteoroids are quite small. Calculate the kinetic energy of a meteoroid of mass \(5.0 \mathrm{g}\) moving at a speed of $48 \mathrm{km} / \mathrm{s}$ and compare it to the kinetic energy of a 1100 -kg car moving at \(29 \mathrm{m} / \mathrm{s}(65 \mathrm{mi} / \mathrm{h})\).

Short answer

Explain your answer. Answer: The meteoroid has more kinetic energy than the car. This is because the kinetic energy of the meteoroid (5.76 * 10^9 J) is much larger than the kinetic energy of the car (463915 J), even though the meteoroid has a smaller mass. This difference is mainly due to the significantly higher speed of the meteoroid compared to the car.

Step-by-step solution

Convert units for mass and speed

The mass of the meteoroid is given in grams, so we need to convert it to kilograms. The speed of the meteoroid is in kilometers per second, so we need to convert it to meters per second. 1 g = 0.001 kg and 1 km/s = 1000 m/s. So, \(m_{meteoroid} = 5.0 \mathrm{g} * 0.001 = 0.005 \mathrm{kg}\) \(v_{meteoroid} = 48 \mathrm{km/s} * 1000 = 48000 \mathrm{m/s}\)

Calculate the kinetic energies for the meteoroid and the car

Now, let's plug in the values into the kinetic energy formula for both the meteoroid and the car. Meteoroid: \(KE_{meteoroid} = \frac{1}{2} * 0.005 \mathrm{kg} * (48000 \mathrm{m/s})^2\) Car: \(KE_{car} = \frac{1}{2} * 1100 \mathrm{kg} * (29 \mathrm{m/s})^2\)

Calculate the values for the kinetic energies

Now let's find the actual values for the kinetic energies of the meteoroid and the car: \(KE_{meteoroid} = \frac{1}{2} * 0.005 \mathrm{kg} * (48000 \mathrm{m/s})^2 = 5.76 * 10^9 \mathrm{J}\) \(KE_{car} = \frac{1}{2} * 1100 \mathrm{kg} * (29 \mathrm{m/s})^2 = 463915 \mathrm{J}\)

Compare the kinetic energies

Finally, let's compare the kinetic energies of the meteoroid and the car: \(KE_{meteoroid} = 5.76 * 10^9\ \mathrm{J}\) \(KE_{car} = 463915\ \mathrm{J}\) The kinetic energy of the meteoroid is much larger than the kinetic energy of the car, despite its smaller mass. This is due to the significantly higher speed at which the meteoroid is moving.