How to Calculate the Magnitude of Acceleration of a 13-year-old Student for an Object with 3 Forces Acting Through its Center of Mass

Step-by-Step Explanation on Finding the Magnitude of Acceleration

Imagine you have an object with mass 0.5 kg, and there are three forces acting on it through its center of mass. Two of these forces are given: one is 7 N to the right, and another is 9 N to the left. We want to find the magnitude of the acceleration.

Step 1: Understand the Forces and Directions

• Force to the right = +7 N (positive direction)
• Force to the left = -9 N (negative direction because it is opposite)
• The third force is not given, so we will call it F₃ (you need to know this or it is zero if not mentioned).

Step 2: Calculate the Net Force

Net force (F_net) is the sum of all forces acting on the object, taking direction into account:

F_net = Force_right + Force_left + Force₃

If the third force is zero, then:

F_net = 7 N (right) + (-9 N) (left) + 0 = -2 N

Because the net force is negative, it means the total force is 2 N to the left.

Step 3: Use Newton's Second Law to Find Acceleration

Newton’s second law says:

F = m × a

where F is the net force, m is the mass, and a is the acceleration.

Rearranged to find a:

a = F / m

Step 4: Plug in the Values

Plug in the mass and net force:

a = (-2 N) / 0.5 kg = -4 m/s²

Step 5: Find the Magnitude of Acceleration

The magnitude of acceleration means the size or amount without considering direction, so:

magnitude of a = 4 m/s²

Summary:

• Find net force by adding up all forces (consider directions).
• Use F = m × a to solve for acceleration.
• Take the absolute value to find the magnitude.

If you get the value of the third force, just include it in the net force sum and follow the steps the same way!