Question
Math Equation Response Question
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.
Force (N) Acceleration (m/s2)
10 0.5
24 1.2
30 1.5
Based on the recorded observations, what is the mass of the go-cart in kilograms?
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.
Force (N) Acceleration (m/s2)
10 0.5
24 1.2
30 1.5
Based on the recorded observations, what is the mass of the go-cart in kilograms?
Answers
GPT-4o mini
To find the mass of the go-cart, we can use Newton's second law of motion, which states that:
\[ F = m \cdot a \]
where:
- \( F \) is the force in newtons (N),
- \( m \) is the mass in kilograms (kg),
- \( a \) is the acceleration in meters per second squared (m/s²).
From the data provided, we can use any of the sets of values for force and acceleration to calculate the mass. Let's take the first set of data (Force = 10 N, Acceleration = 0.5 m/s²):
1. Rearranging the formula for mass:
\[ m = \frac{F}{a} \]
2. Plugging in the values:
\[ m = \frac{10 \, \text{N}}{0.5 \, \text{m/s}^2} \]
3. Calculating:
\[ m = 20 \, \text{kg} \]
Now, let's verify the mass using the second set of data (Force = 24 N, Acceleration = 1.2 m/s²):
1. Using the formula for mass:
\[ m = \frac{F}{a} \]
2. Plugging in the values:
\[ m = \frac{24 \, \text{N}}{1.2 \, \text{m/s}^2} \]
3. Calculating:
\[ m = 20 \, \text{kg} \]
Finally, let's check the third set of data (Force = 30 N, Acceleration = 1.5 m/s²):
1. Using the formula for mass:
\[ m = \frac{F}{a} \]
2. Plugging in the values:
\[ m = \frac{30 \, \text{N}}{1.5 \, \text{m/s}^2} \]
3. Calculating:
\[ m = 20 \, \text{kg} \]
From all three calculations, we find that the mass of the go-cart is consistently:
**20 kg**.
\[ F = m \cdot a \]
where:
- \( F \) is the force in newtons (N),
- \( m \) is the mass in kilograms (kg),
- \( a \) is the acceleration in meters per second squared (m/s²).
From the data provided, we can use any of the sets of values for force and acceleration to calculate the mass. Let's take the first set of data (Force = 10 N, Acceleration = 0.5 m/s²):
1. Rearranging the formula for mass:
\[ m = \frac{F}{a} \]
2. Plugging in the values:
\[ m = \frac{10 \, \text{N}}{0.5 \, \text{m/s}^2} \]
3. Calculating:
\[ m = 20 \, \text{kg} \]
Now, let's verify the mass using the second set of data (Force = 24 N, Acceleration = 1.2 m/s²):
1. Using the formula for mass:
\[ m = \frac{F}{a} \]
2. Plugging in the values:
\[ m = \frac{24 \, \text{N}}{1.2 \, \text{m/s}^2} \]
3. Calculating:
\[ m = 20 \, \text{kg} \]
Finally, let's check the third set of data (Force = 30 N, Acceleration = 1.5 m/s²):
1. Using the formula for mass:
\[ m = \frac{F}{a} \]
2. Plugging in the values:
\[ m = \frac{30 \, \text{N}}{1.5 \, \text{m/s}^2} \]
3. Calculating:
\[ m = 20 \, \text{kg} \]
From all three calculations, we find that the mass of the go-cart is consistently:
**20 kg**.