In a series of controlled experiments, a student measures the force acting on a go-cart and the go-cart's acceleration. The student's data are shown below.

Question

force aceleration
10 0.5
24 1.2
30 1.5

Based on the recorded observations, what is the mass of the go-cart in kilograms? (F=ma)

a
45 kg
b
28.8 kg
c
5 kg
d
20 kg

Answer 1

To determine the mass of the go-cart using the formula \( F = ma \), we can rearrange the equation to solve for mass:

\[ m = \frac{F}{a} \]

We can use any of the data points provided to find the mass. Let's use the first data point:

1. For \( F = 10 , \text{N} \) and \( a = 0.5 , \text{m/s}^2 \): \[ m = \frac{10 , \text{N}}{0.5 , \text{m/s}^2} = \frac{10}{0.5} = 20 , \text{kg} \]

Now, let's verify this with the other data points to ensure they yield the same mass.

2. For \( F = 24 , \text{N} \) and \( a = 1.2 , \text{m/s}^2 \): \[ m = \frac{24 , \text{N}}{1.2 , \text{m/s}^2} = \frac{24}{1.2} = 20 , \text{kg} \]

3. For \( F = 30 , \text{N} \) and \( a = 1.5 , \text{m/s}^2 \): \[ m = \frac{30 , \text{N}}{1.5 , \text{m/s}^2} = \frac{30}{1.5} = 20 , \text{kg} \]

In all cases, the mass of the go-cart is the same. Therefore, the mass of the go-cart is:

d) 20 kg.