To find the mass of the cart, we can use Newton's second law of motion, which states that \( F = m \cdot a \), where \( F \) is the force applied, \( m \) is the mass, and \( a \) is the acceleration.
We can rearrange the formula to find mass:
\[ m = \frac{F}{a} \]
Let's use the data from the first trial to find the mass:
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Trial 1:
- Force \( F = 10 , \text{N} \)
- Acceleration \( a = 2.5 , \text{m/s}^2 \)
\[ m = \frac{10, \text{N}}{2.5 , \text{m/s}^2} = 4 , \text{kg} \]
Now, let's verify this mass with the other trials:
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Trial 2:
- Force \( F = 12 , \text{N} \)
- Acceleration \( a = 3 , \text{m/s}^2 \)
\[ m = \frac{12 , \text{N}}{3 , \text{m/s}^2} = 4 , \text{kg} \]
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Trial 3:
- Force \( F = 22 , \text{N} \)
- Acceleration \( a = 5.5 , \text{m/s}^2 \)
\[ m = \frac{22 , \text{N}}{5.5 , \text{m/s}^2} = 4 , \text{kg} \]
In all trials, the mass of the cart calculated is \( 4 , \text{kg} \).
Therefore, the mass of the cart is:
b. 4 kg.
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