How to Find the Magnitude of Acceleration of a 0.5 kg Object with 3 Forces Acting at the Center of Mass for a 13-Year-Old

Step-by-step Explanation: Finding the Magnitude of Acceleration

Let's break down the problem step by step.

Given:

• Mass of object, m = 0.5 kg
• Forces acting to the right: 3 N and 4 N
• Force acting to the left: 9 N

Step 1: Understand the direction of forces

We have two forces pulling (or pushing) to the right and one force pushing to the left. Since forces have directions, we can consider right as positive (+) and left as negative (−).

Step 2: Calculate the net force

Add the forces, keeping track of the direction:

• Forces to the right: 3 N + 4 N = 7 N (positive direction)
• Force to the left: -9 N (negative direction)

Net force, F_net = 7 N + (-9 N) = -2 N

The negative sign means the net force is to the left.

Step 3: Use Newton's Second Law to find acceleration

Newton's Second Law states:

F_net = m × a

If we want to find acceleration, rearrange the formula:

a = F_net / m

Step 4: Calculate the magnitude of acceleration

Substitute values:

a = (-2 N) / 0.5 kg = -4 m/s²

Step 5: Find the magnitude (size) of acceleration

Magnitude is always positive, so:

|a| = 4 m/s²

Summary:

The net force points to the left with 2 N, and the object accelerates to the left with an acceleration magnitude of 4 meters per second squared.