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.

Question

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 determine 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 \( F = ma \), where \( F \) is the force, \( m \) is the mass of the cart, and \( a \) is the acceleration.

From the data provided, we can first calculate the mass of the cart using the forces and the corresponding accelerations that we have.

Using the data point for \( 1 , \text{N} \) and \( 0.2 , \text{m/s}^2 \):

\[ 1 = m \times 0.2 \]

Solving for \( m \):

\[ m = \frac{1}{0.2} = 5 , \text{kg} \]

Now that we have the mass of the cart, we can find the force needed to achieve an acceleration of \( 2.6 , \text{m/s}^2 \):

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

Thus, the force acting on the cart when the acceleration is \( 2.6 , \text{m/s}^2 \) is 13 N.