Question

Question 31
Trial Force (N) Acceleration (m/s^2)
1 10 N 2.5
2 12 3
3 22 5.5
Students are running an experiment in which they are measuring the acceleration after applying forces to a cart. Using the data above, what is the mass of the cart?

a
2 kg
b
4 kg
c
6 kg
d
8 kg

Answer 1

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, \( m \) is the mass, and \( a \) is the acceleration.

We can rearrange the formula to solve for mass \( m \):
\[
m = \frac{F}{a}
\]

We can use any of the trials provided to calculate the mass. Let's use Trial 1 as an example:

**Trial 1:**
- Force (F) = 10 N
- Acceleration (a) = 2.5 m/s²

Now, we can calculate the mass:
\[
m = \frac{10 \, \text{N}}{2.5 \, \text{m/s}^2} = 4 \, \text{kg}
\]

We can check if this mass is consistent with the other trials:

**Trial 2:**
- Force (F) = 12 N
- Acceleration (a) = 3 m/s²
\[
m = \frac{12 \, \text{N}}{3 \, \text{m/s}^2} = 4 \, \text{kg}
\]

**Trial 3:**
- Force (F) = 22 N
- Acceleration (a) = 5.5 m/s²
\[
m = \frac{22 \, \text{N}}{5.5 \, \text{m/s}^2} = 4 \, \text{kg}
\]

The mass calculated from all trials is consistently 4 kg.

Thus, the mass of the cart is:
**b. 4 kg**