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Answer :
To find out how much more kinetic energy the 6-kilogram bowling ball has when rolling at 16 mph compared to 14 mph, we can use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( v \)[/tex] is the velocity of the object.
Step-by-step solution:
1. Identify the mass and velocities:
- Mass ([tex]\( m \)[/tex]) of the bowling ball is 6 kilograms.
- Velocity 1 ([tex]\( v_1 \)[/tex]) is 7.1 meters per second (equivalent to 16 mph).
- Velocity 2 ([tex]\( v_2 \)[/tex]) is 6.2 meters per second (equivalent to 14 mph).
2. Calculate the kinetic energy at 16 mph (7.1 m/s):
[tex]\[ KE_1 = \frac{1}{2} \times 6 \times (7.1)^2 \][/tex]
When you calculate this, you get approximately 151.23 Joules.
3. Calculate the kinetic energy at 14 mph (6.2 m/s):
[tex]\[ KE_2 = \frac{1}{2} \times 6 \times (6.2)^2 \][/tex]
After calculating this, you will have approximately 115.32 Joules.
4. Find the difference in kinetic energy:
[tex]\[ KE_{\text{difference}} = KE_1 - KE_2 \][/tex]
[tex]\[ KE_{\text{difference}} = 151.23 - 115.32 \][/tex]
This gives you approximately 35.91 Joules.
Therefore, the bowling ball has approximately 35.91 Joules more kinetic energy when rolling at 16 mph compared to when it's rolling at 14 mph. The closest option to this calculation is 35.9 J.
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( v \)[/tex] is the velocity of the object.
Step-by-step solution:
1. Identify the mass and velocities:
- Mass ([tex]\( m \)[/tex]) of the bowling ball is 6 kilograms.
- Velocity 1 ([tex]\( v_1 \)[/tex]) is 7.1 meters per second (equivalent to 16 mph).
- Velocity 2 ([tex]\( v_2 \)[/tex]) is 6.2 meters per second (equivalent to 14 mph).
2. Calculate the kinetic energy at 16 mph (7.1 m/s):
[tex]\[ KE_1 = \frac{1}{2} \times 6 \times (7.1)^2 \][/tex]
When you calculate this, you get approximately 151.23 Joules.
3. Calculate the kinetic energy at 14 mph (6.2 m/s):
[tex]\[ KE_2 = \frac{1}{2} \times 6 \times (6.2)^2 \][/tex]
After calculating this, you will have approximately 115.32 Joules.
4. Find the difference in kinetic energy:
[tex]\[ KE_{\text{difference}} = KE_1 - KE_2 \][/tex]
[tex]\[ KE_{\text{difference}} = 151.23 - 115.32 \][/tex]
This gives you approximately 35.91 Joules.
Therefore, the bowling ball has approximately 35.91 Joules more kinetic energy when rolling at 16 mph compared to when it's rolling at 14 mph. The closest option to this calculation is 35.9 J.
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