To find the difference in kinetic energy when a bowling ball is rolling at different speeds, we can first calculate the kinetic energy (KE) at both speeds using the formula:
\[ KE = \frac{1}{2}mv^2 \]
Where \(m\) is the mass (6 kg) and \(v\) is the velocity.
- Kinetic Energy at 16 mph (7.1 meters per second):
\[ KE_{16} = \frac{1}{2} \times 6 , \text{kg} \times (7.1 , \text{m/s})^2 \]
Calculating \( (7.1 , \text{m/s})^2 \):
\[ (7.1)^2 = 50.41 \]
So,
\[ KE_{16} = \frac{1}{2} \times 6 \times 50.41 = 3 \times 50.41 = 151.23 , \text{J} \]
- Kinetic Energy at 14 mph (6.2 meters per second):
\[ KE_{14} = \frac{1}{2} \times 6 , \text{kg} \times (6.2 , \text{m/s})^2 \]
Calculating \( (6.2 , \text{m/s})^2 \):
\[ (6.2)^2 = 38.44 \]
So,
\[ KE_{14} = \frac{1}{2} \times 6 \times 38.44 = 3 \times 38.44 = 115.32 , \text{J} \]
- Difference in Kinetic Energy:
\[ \Delta KE = KE_{16} - KE_{14} = 151.23 , \text{J} - 115.32 , \text{J} = 35.91 , \text{J} \]
Thus, the bowling ball has 35.9 J more kinetic energy when rolling at 16 mph than when rolling at 14 mph.
Answer: 35.9 J