To determine which falling object will result in the least kinetic energy upon colliding with the ground, we can use the formula for kinetic energy (KE):
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
Let's calculate the kinetic energy for each of the given options:
-
100 grams of water falling at 10 m/s
- Mass (m) = 0.1 kg (100 grams)
- Velocity (v) = 10 m/s
- \( KE = \frac{1}{2} \times 0.1 \times (10^2) = \frac{1}{2} \times 0.1 \times 100 = 5 , \text{Joules} \)
-
100 grams of dirt falling at 15 m/s
- Mass (m) = 0.1 kg (100 grams)
- Velocity (v) = 15 m/s
- \( KE = \frac{1}{2} \times 0.1 \times (15^2) = \frac{1}{2} \times 0.1 \times 225 = 11.25 , \text{Joules} \)
-
10 grams of water falling at 1 m/s
- Mass (m) = 0.01 kg (10 grams)
- Velocity (v) = 1 m/s
- \( KE = \frac{1}{2} \times 0.01 \times (1^2) = \frac{1}{2} \times 0.01 \times 1 = 0.005 , \text{Joules} \)
-
10 grams of dirt falling at 2 m/s
- Mass (m) = 0.01 kg (10 grams)
- Velocity (v) = 2 m/s
- \( KE = \frac{1}{2} \times 0.01 \times (2^2) = \frac{1}{2} \times 0.01 \times 4 = 0.02 , \text{Joules} \)
Now, let's summarize the kinetic energies:
- 100 g of water at 10 m/s: 5 Joules
- 100 g of dirt at 15 m/s: 11.25 Joules
- 10 g of water at 1 m/s: 0.005 Joules
- 10 g of dirt at 2 m/s: 0.02 Joules
The falling object with the least kinetic energy when it collides with the ground is:
10 grams of water falling at 1 m/s (0.005 Joules).
1 answer