Calculate the kinetic energy of an object with a mass of \(1.0 \times\) \(10^{-5} \mathrm{~g}\) and a velocity of \(2.0 \times 10^{5} \mathrm{~cm} / \mathrm{s}\)

Short Answer

Expert verified
The kinetic energy of the object with a mass of \(1.0 \times 10^{-8} \mathrm{~kg}\) and a velocity of \(2.0 \times 10^{3} \mathrm{~m/s}\) is \(8.0 \times 10^{-2} \mathrm{~J}\) (Joules).

Step by step solution

01

Convert the given mass and velocity to standard units

To convert mass from grams to kilograms, we will divide by 1000. To convert velocity from centimeters per second to meters per second, we will divide by 100. Mass in kg: \(1.0 \times 10^{-5}\mathrm{~g} = 1.0 \times 10^{-5}\mathrm{~g} \times \frac{1\mathrm{~kg}}{1000\mathrm{~g}} = 1.0 \times 10^{-8}\mathrm{~kg}\) Velocity in m/s: \(2.0 \times 10^{5}\mathrm{~cm/s} = 2.0 \times 10^{5}\mathrm{~cm/s} \times \frac{1\mathrm{~m}}{100\mathrm{~cm}} = 2.0 \times 10^{3}\mathrm{~m/s}\)
02

Calculation of kinetic energy

Now that we have the mass and velocity in standard units, we can use the kinetic energy formula: K.E. = 0.5 * m * v^2 Substitute the values: K.E. = 0.5 * \(1.0 \times 10^{-8}\mathrm{~kg}\) * \((2.0 \times 10^{3}\mathrm{~m/s})^2\)
03

Simplify and compute the kinetic energy

Calculate the square of the velocity and then multiply by the mass and 0.5. K.E. = 0.5 * \(1.0 \times 10^{-8}\mathrm{~kg}\) * \((4.0 \times 10^{6}\mathrm{~(m/s)^2})\) K.E. = \(2.0 \times 10^{-8}\mathrm{~kg} \times 4.0 \times 10^{6}\mathrm{~(m/s)^2}\) K.E. = \(8.0 \times 10^{-2}\mathrm{~J}\) (Joules) The kinetic energy of the object is 8.0 x 10^{-2} Joules.

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Most popular questions from this chapter

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