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 bew. According to the data table, how much force is acting on the cart when the students measure an acceleration of 2.6 m/s²? (*Hint: the cart is the same cart for each trial).
[Force acting on cart N](Cart Acceleration m/s^2)
[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 that:

\[ F = m \cdot a \]

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

First, we can find the mass of the cart using the existing data from the table.

From the data given, we can select a pair of values to solve for the mass \( m \). Let's take the first data point:

1. For \( F = 1 \) N, the acceleration \( a = 0.2 \) m/s²:

Using the formula:
\[ 1 = m \cdot 0.2 \]
Thus,
\[ m = \frac{1}{0.2} = 5 \, \text{kg} \]

Now we'll use the mass to find the force at the acceleration of 2.6 m/s².

Using the mass \( m = 5 \) kg and \( a = 2.6 \) m/s²:

\[ F = 5 \cdot 2.6 = 13 \, \text{N} \]

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