To understand the meaning of the symbol [tex]\(\Sigma F\)[/tex] in the formula [tex]\(a = \frac{\Sigma F}{m}\)[/tex], let's break down the components included in Newton's second law.
1. Formula Interpretation:
- Newton's second law of motion is given by [tex]\(a = \frac{F}{m}\)[/tex], where [tex]\(a\)[/tex] is the acceleration, [tex]\(F\)[/tex] is the net force acting on the object, and [tex]\(m\)[/tex] is the mass of the object.
- In the modified formula provided, [tex]\(a = \frac{\Sigma F}{m}\)[/tex], the symbol [tex]\(\Sigma F\)[/tex] is used. The Greek letter "Sigma" (Σ) typically represents the summation of quantities.
2. Meaning of [tex]\(\Sigma F\)[/tex]:
- [tex]\(\Sigma F\)[/tex] signifies the sum of all forces acting on the object.
- These forces can include various components such as horizontal forces, vertical forces, or any force applied in different directions on the object.
3. Application:
- To find [tex]\(\Sigma F\)[/tex], you indeed need to consider all forces acting on the object.
- Forces may act in different directions (horizontal and vertical), making it essential to combine these various force components to find the total or net force acting on the object.
4. Choices Analysis:
- He needs to find the net force acting on the object in a direction: This is true but does not capture the complete meaning of [tex]\(\Sigma F\)[/tex].
- He needs to use only forces acting in the direction of motion: This is not accurate as [tex]\(\Sigma F\)[/tex] includes all forces irrespective of their direction.
- He needs to combine the horizontal and vertical forces: This is correct as [tex]\(\Sigma F\)[/tex] involves summing up all the forces from different directions to get the net force.
- He needs to multiply the horizontal and vertical forces: This is incorrect because multiplication of forces is not involved in [tex]\(\Sigma F\)[/tex].
Based on the detailed analysis, the symbol [tex]\(\Sigma F\)[/tex] in the formula indicates that Chang needs to combine the horizontal and vertical forces. Therefore, the correct choice is:
He needs to combine the horizontal and vertical forces.
