To complete the data table you've provided for the simulation with the different combinations of fans and blocks, we must first determine the total force acting on the cart, the total mass (including the mass of the blocks), and then calculate the acceleration using Newton's second law, \( F = ma \).
Let's fill in the table:
Assumptions:
- Each fan exerts a force of \( 4.0 , \text{N} \).
- The following are assumed masses:
- Each block has a mass of \( 1 , \text{kg} \) (for example).
- The cart itself may have a mass (you should check the simulation for this value; let's assume it's 2 kg for this example).
1. For 2 fans, 0 blocks:
- Force: \( 2 , \text{fans} \times 4.0 , \text{N/fan} = 8.0 , \text{N} \)
- Mass: \( 2 , \text{kg (cart)} + 0 , \text{kg (blocks)} = 2 , \text{kg} \)
- Acceleration: \( a = \frac{F}{m} = \frac{8.0 , \text{N}}{2 , \text{kg}} = 4.0 , \text{m/s}^2 \)
- \( m \cdot a = 2 , \text{kg} \times 4.0 , \text{m/s}^2 = 8.0 \)
2. For 1 fan, 2 blocks:
- Force: \( 1 , \text{fan} \times 4.0 , \text{N/fan} = 4.0 , \text{N} \)
- Mass: \( 2 , \text{kg (cart)} + 2 , \text{kg (blocks)} = 4 , \text{kg} \)
- Acceleration: \( a = \frac{F}{m} = \frac{4.0 , \text{N}}{4 , \text{kg}} = 1.0 , \text{m/s}^2 \)
- \( m \cdot a = 4 , \text{kg} \times 1.0 , \text{m/s}^2 = 4.0 \)
3. For 3 fans, 1 block:
- Force: \( 3 , \text{fans} \times 4.0 , \text{N/fan} = 12.0 , \text{N} \)
- Mass: \( 2 , \text{kg (cart)} + 1 , \text{kg (block)} = 3 , \text{kg} \)
- Acceleration: \( a = \frac{F}{m} = \frac{12.0 , \text{N}}{3 , \text{kg}} = 4.0 , \text{m/s}^2 \)
- \( m \cdot a = 3 , \text{kg} \times 4.0 , \text{m/s}^2 = 12.0 \)
Final Data Table:
| Load | #Fans on | Force (N) | Mass (kg) | Acceleration (m/s²) | \( m \cdot a \) (N) | |----------------|----------|------------|-----------|----------------------|----------------------| | 2 fans, 0 blocks | 2 | 8.0 | 2 | 4.0 | 8.0 | | 1 fan, 2 blocks | 1 | 4.0 | 4 | 1.0 | 4.0 | | 3 fans, 1 block | 3 | 12.0 | 3 | 4.0 | 12.0 |
Feel free to input the actual values from your simulation, as the mass of the cart or blocks may differ.
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