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Chapter 6: Problem 30

Which has the greater kinetic energy, an object with a mass of 2.0 \(\mathrm{kg}\) and a velocity of 1.0 \(\mathrm{m} / \mathrm{s}\) or an object with a mass of 1.0 \(\mathrm{kg}\) and a velocity of 2.0 $\mathrm{m} / \mathrm{s}$ ?

Short Answer

Expert verified
The object with a mass of 1.0 kg and a velocity of 2.0 m/s has greater kinetic energy (2.0 J) than the object with a mass of 2.0 kg and a velocity of 1.0 m/s (1.0 J).

Step by step solution

01

Object 1: Calculate Kinetic Energy

Using the given formula, we can compute the kinetic energy of object 1: \( KE_1 = \frac{1}{2} \times 2.0 \, kg \times (1.0 \, m/s)^2 \)
02

Object 1: Simplify and Calculate

Now, we simplify the expression and calculate the kinetic energy: \( KE_1 = 1.0\, kg \times 1.0 \, m^2/s^2 = 1.0 \, J \) where J represents joules, the unit of energy.
03

Object 2: Calculate Kinetic Energy

Similarly, we can compute the kinetic energy of object 2: \( KE_2 = \frac{1}{2} \times 1.0\, kg \times (2.0\, m/s)^2 \)
04

Object 2: Simplify and Calculate

After simplifying this expression and calculating the kinetic energy: \( KE_2 = 0.5 \, kg \times 4.0 \, m^2/s^2 = 2.0 \, J \)
05

Compare Kinetic Energies

Now we compare the kinetic energies of both objects: \( KE_1 = 1.0 \, J \) \( KE_2 = 2.0 \, J \) Since \( KE_2 > KE_1 \), the object with a mass of 1.0 kg and a velocity of 2.0 m/s has greater kinetic energy than the object with a mass of 2.0 kg and a velocity of 1.0 m/s.

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