Question

Some students measure the acceleration of a wheeled cart being acted on by varying forces. The students record their data in the table shown below.
According to the data table, how much force is acting on the cart when the students measure an acceleration of 2.6 m/s?? (*Hint: the cart is the same cart for each trial).
HINT: Refer to your STAAR Reference Sheet.
Force Acting on Cart
(N)
Cart Acceleration (m/s')
1
0.2
2
0.4
5
1.0
6
1.2
?
2.6

Answer 1

To find the force acting on the cart when the acceleration is 2.6 m/s², we can use Newton's second law of motion, which states:

\[ F = m \cdot a \]

Where:
- \( F \) is the force,
- \( m \) is the mass of the object,
- \( a \) is the acceleration.

First, we need to calculate the mass of the cart using the data provided. We can use any of the existing data points to find the mass.

From the first pair of data:
- When the force is 1 N, the acceleration is 0.2 m/s².

Using this data point, we can find the mass:

\[
m = \frac{F}{a} = \frac{1 \, \text{N}}{0.2 \, \text{m/s}^2} = 5 \, \text{kg}
\]

Now that we have the mass of the cart, we can calculate the force acting on the cart for an acceleration of 2.6 m/s²:

\[
F = m \cdot a = 5 \, \text{kg} \cdot 2.6 \, \text{m/s}^2 = 13 \, \text{N}
\]

Therefore, the force acting on the cart when the students measure an acceleration of 2.6 m/s² is **13 N**.