To analyze the acceleration values based on the given scenario, we can break down the answers for each of the questions.
5A. How did doubling the force affect the acceleration of the cart?
According to Newton's second law of motion, \( F = ma \), where \( F \) is the force applied, \( m \) is the mass of the object, and \( a \) is the acceleration. When you double the force while keeping the mass constant, the acceleration will also double. For example, if the original force is 4 N, and the resulting acceleration is \( a_1 \), when you double the force to 8 N, the new acceleration \( a_2 \) would be \( 2 \times a_1 \).
6B. What do you notice about the force and the product of mass and acceleration, ma?
The product of mass and acceleration \( ma \) is equal to the net force applied \( F \). This means that for any given system, the net force is directly proportional to the mass of the object it is acting on and the resulting acceleration. If the force increases, the product \( ma \) also increases, and vice versa, as indicated by the relationship \( F = ma \).
8. What will be the acceleration of the cart?
Given:
- The cart contains 2 fans, each supplying a force of 4.0 N.
- Total mass of the cart = 22.5 kg.
First, calculate the total force exerted by the fans:
\[ \text{Total Force} = \text{Number of Fans} \times \text{Force per Fan} = 2 \times 4.0 , \text{N} = 8.0 , \text{N} \]
Now, using Newton's second law \( F = ma \) to find the acceleration \( a \):
\[ a = \frac{F}{m} = \frac{8.0 , \text{N}}{22.5 , \text{kg}} \approx 0.356 , \text{m/s}^2 \]
Thus, the acceleration of the cart will be approximately 0.356 m/s².
Check your answer using the Gizmo.
Make sure to input the same data into the Gizmo to verify your calculations and see if you get the same acceleration value. Depending on the setup of the Gizmo, you should confirm whether it reflects the approximate acceleration of 0.356 m/s² based on your inputs.