High School

Calculate the kinetic energies (in J) of the following:

(a) A 2,004.0 kg automobile moving at 140.0 km/h.

(b) An 84 kg runner sprinting at 12 m/s.

(c) A [tex]9.1 \times 10^{-31}[/tex] kg electron moving at [tex]2.2 \times 10^{7}[/tex] m/s.

Answer :

(a) To calculate the kinetic energy of the automobile, we first need to convert its speed from km/h to m/s:
140.0 km/h = 38.89 m/s

The kinetic energy is then calculated using the formula KE = 1/2mv^2, where m is the mass in kg and v is the velocity in m/s.

KE = 1/2 x 2,004.0 kg x (38.89 m/s)^2
KE = 1.2 x 10^7 J

Therefore, the kinetic energy of the automobile is 1.2 x 10^7 J.

(b) To calculate the kinetic energy of the runner, we use the same formula:

KE = 1/2 x 84 kg x (12 m/s)^2
KE = 6,048 J

Therefore, the kinetic energy of the runner is 6,048 J.

(c) To calculate the kinetic energy of the electron, we use the formula KE = 1/2mv^2, where m is the mass in kg and v is the velocity in m/s.

KE = 1/2 x 9.1 x 10^-31 kg x (2.2 x 10^7 m/s)^2
KE = 2.0 x 10^-14 J

Therefore, the kinetic energy of the electron is 2.0 x 10^-14 J.

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