Question

an object has a velocity of 8 m/s and a kinetic energy of 480 j. what is the mass of the object? (formula: ( ke = \frac{1}{2}mv^2 ))

7.5 kg
15 kg
60 kg
120 kg

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), where \( KE \) is kinetic energy, \( m \) is mass, and \( v \) is velocity. We need to solve for \( m \), so we can rearrange the formula.
First, multiply both sides of the equation by 2 to get rid of the fraction: \( 2KE = mv^2 \).

Step2: Solve for mass \( m \)

Then, divide both sides by \( v^2 \) to isolate \( m \). The formula becomes \( m=\frac{2KE}{v^2} \).
We know that \( KE = 480 \, \text{J} \) and \( v = 8 \, \text{m/s} \). Substitute these values into the formula:
\( m=\frac{2\times480}{8^2} \)
First, calculate the numerator: \( 2\times480 = 960 \).
Then, calculate the denominator: \( 8^2=64 \).
Now, divide the numerator by the denominator: \( m = \frac{960}{64}=15 \, \text{kg} \).

Answer:

15 kg (corresponding to the option "15 kg")