Questions: Calculate the kinetic energies (in J) of the following. (a) a 2,002.0 kg automobile moving at 130.0 km/h J (b) an 84 kg runner sprinting at 13 m/s J (c) a 9.1 x 10^-31 kg electron moving at 2.3 x 10^7 m/s J

Calculate the kinetic energies (in J) of the following.
(a) a 2,002.0 kg automobile moving at 130.0 km/h
 J
(b) an 84 kg runner sprinting at 13 m/s
 J
(c) a 9.1 x 10^-31 kg electron moving at 2.3 x 10^7 m/s
 J
Transcript text: Calculate the kinetic energies (in J) of the following. (a) a 2,002.0 kg automobile moving at $130.0 \cdot \mathrm{~km} / \mathrm{h}$ $\square$ J (b) an 84 kg runner sprinting at $13 \mathrm{~m} / \mathrm{s}$ $\square$ J (c) a $9.1 \times 10^{-31} \mathrm{~kg}$ electron moving at $2.3 \times 10^{7} \mathrm{~m} / \mathrm{s}$ $\square$ J
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Solution

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Solution Steps

Step 1: Convert the speed of the automobile to meters per second

The speed of the automobile is given in km/h. We need to convert this to m/s.

130.0km/h=130.0×1000m1km×1h3600s=36.1111m/s 130.0 \, \text{km/h} = 130.0 \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 36.1111 \, \text{m/s}

Step 2: Calculate the kinetic energy of the automobile

The kinetic energy K K is given by the formula:

K=12mv2 K = \frac{1}{2} m v^2

For the automobile:

K=12×2002.0kg×(36.1111m/s)2=1.305×106J K = \frac{1}{2} \times 2002.0 \, \text{kg} \times (36.1111 \, \text{m/s})^2 = 1.305 \times 10^6 \, \text{J}

Step 3: Calculate the kinetic energy of the runner

Using the same kinetic energy formula for the runner:

K=12×84kg×(13m/s)2=7107J K = \frac{1}{2} \times 84 \, \text{kg} \times (13 \, \text{m/s})^2 = 7107 \, \text{J}

Step 4: Calculate the kinetic energy of the electron

Using the kinetic energy formula for the electron:

K=12×9.1×1031kg×(2.3×107m/s)2=2.404×1016J K = \frac{1}{2} \times 9.1 \times 10^{-31} \, \text{kg} \times (2.3 \times 10^7 \, \text{m/s})^2 = 2.404 \times 10^{-16} \, \text{J}

Final Answer

(a) The kinetic energy of the automobile is 1.305×106J\boxed{1.305 \times 10^6 \, \text{J}}.

(b) The kinetic energy of the runner is 7107J\boxed{7107 \, \text{J}}.

(c) The kinetic energy of the electron is 2.404×1016J\boxed{2.404 \times 10^{-16} \, \text{J}}.

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