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Answer :
Sure! To find out how much more kinetic energy a 6-kilogram bowling ball has when rolling at 16 mph compared to 14 mph, we can use the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} m v^2, \][/tex]
where [tex]\( m \)[/tex] is the mass of the object and [tex]\( v \)[/tex] is its velocity.
Step 1: Calculate the kinetic energy at 16 mph
Given:
- Mass [tex]\( m = 6 \)[/tex] kg
- Velocity [tex]\( v_1 = 7.1 \)[/tex] m/s (conversion of 16 mph to meters per second)
Substitute these values into the kinetic energy formula:
[tex]\[ KE_1 = \frac{1}{2} \times 6 \times (7.1)^2. \][/tex]
Perform the calculation:
[tex]\[ KE_1 = 3 \times 50.41 = 151.23 \text{ J}. \][/tex]
Step 2: Calculate the kinetic energy at 14 mph
Given:
- Velocity [tex]\( v_2 = 6.2 \)[/tex] m/s (conversion of 14 mph to meters per second)
Substitute these values into the kinetic energy formula:
[tex]\[ KE_2 = \frac{1}{2} \times 6 \times (6.2)^2. \][/tex]
Perform the calculation:
[tex]\[ KE_2 = 3 \times 38.44 = 115.32 \text{ J}. \][/tex]
Step 3: Find the difference in kinetic energy
Now, subtract the kinetic energy at 14 mph from the kinetic energy at 16 mph:
[tex]\[ KE_{\text{difference}} = KE_1 - KE_2. \][/tex]
[tex]\[ KE_{\text{difference}} = 151.23 \text{ J} - 115.32 \text{ J} = 35.9 \text{ J}. \][/tex]
Thus, the bowling ball has 35.9 joules more kinetic energy when rolling at 16 mph compared to 14 mph. The correct answer is 35.9 J.
[tex]\[ KE = \frac{1}{2} m v^2, \][/tex]
where [tex]\( m \)[/tex] is the mass of the object and [tex]\( v \)[/tex] is its velocity.
Step 1: Calculate the kinetic energy at 16 mph
Given:
- Mass [tex]\( m = 6 \)[/tex] kg
- Velocity [tex]\( v_1 = 7.1 \)[/tex] m/s (conversion of 16 mph to meters per second)
Substitute these values into the kinetic energy formula:
[tex]\[ KE_1 = \frac{1}{2} \times 6 \times (7.1)^2. \][/tex]
Perform the calculation:
[tex]\[ KE_1 = 3 \times 50.41 = 151.23 \text{ J}. \][/tex]
Step 2: Calculate the kinetic energy at 14 mph
Given:
- Velocity [tex]\( v_2 = 6.2 \)[/tex] m/s (conversion of 14 mph to meters per second)
Substitute these values into the kinetic energy formula:
[tex]\[ KE_2 = \frac{1}{2} \times 6 \times (6.2)^2. \][/tex]
Perform the calculation:
[tex]\[ KE_2 = 3 \times 38.44 = 115.32 \text{ J}. \][/tex]
Step 3: Find the difference in kinetic energy
Now, subtract the kinetic energy at 14 mph from the kinetic energy at 16 mph:
[tex]\[ KE_{\text{difference}} = KE_1 - KE_2. \][/tex]
[tex]\[ KE_{\text{difference}} = 151.23 \text{ J} - 115.32 \text{ J} = 35.9 \text{ J}. \][/tex]
Thus, the bowling ball has 35.9 joules more kinetic energy when rolling at 16 mph compared to 14 mph. The correct answer is 35.9 J.
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