Question

a ball rolls across the floor at (8.10\text{ m/s}) has (62.3\text{ j}) of kinetic energy.

what is the mass of the ball?

(m = ?\text{ kg})

Explanation:

⚡ Using what you learned: kinetic energy and the work-energy theorem

Step 1: Identify given values

$$ v = 8.10\text{ m/s} $$

$$ KE = 62.3\text{ J} $$

Step 2: Set up the kinetic energy formula

$$ KE = \frac{1}{2}mv^2 $$

Step 3: Solve for mass \(m\)

$$ m = \frac{2 \cdot KE}{v^2} $$

$$ m = \frac{2 \cdot 62.3}{(8.10)^2} $$

$$ m = \frac{124.6}{65.61} \approx 1.8991\text{ kg} $$

Rounding to three significant figures:

$$ m \approx 1.90\text{ kg} $$

Answer:

1.90