To determine which object will have the greatest kinetic energy when dropped from a height, we can use the formula for gravitational potential energy (which converts to kinetic energy when the object falls):
\[ KE = mgh \]
where:
- \( KE \) = kinetic energy,
- \( m \) = mass of the object (in kilograms),
- \( g \) = acceleration due to gravity (approximately \( 9.81 , m/s^2 \)),
- \( h \) = height (in meters).
We need to convert the mass of each object from grams to kilograms (1 gram = 0.001 kilograms) before substituting them into the formula.
-
Table tennis ball:
- Mass = 2.7 grams = 0.0027 kg
- \( KE = 0.0027 \times 9.81 \times 2 \)
-
Baseball:
- Mass = 147.0 grams = 0.147 kg
- \( KE = 0.147 \times 9.81 \times 2 \)
-
Small rock:
- Mass = 248.2 grams = 0.2482 kg
- \( KE = 0.2482 \times 9.81 \times 2 \)
-
Penny:
- Mass = 2.5 grams = 0.0025 kg
- \( KE = 0.0025 \times 9.81 \times 2 \)
Now we calculate the kinetic energy for each object:
-
Table tennis ball: \[ KE = 0.0027 \times 9.81 \times 2 \approx 0.053 , J \]
-
Baseball: \[ KE = 0.147 \times 9.81 \times 2 \approx 2.89 , J \]
-
Small rock: \[ KE = 0.2482 \times 9.81 \times 2 \approx 4.87 , J \]
-
Penny: \[ KE = 0.0025 \times 9.81 \times 2 \approx 0.049 , J \]
From these calculations, the small rock has the highest kinetic energy (approximately 4.87 J) when dropped from a height of 2 meters.
Therefore, the object that will have the greatest kinetic energy is the small rock.
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