Physics 5054/11 — October/November 2014

Walkthrough

To find the direction of the resultant force, we resolve the two forces into horizontal and vertical components.

1. The 25 N force points upward and to the right. This means it has a positive horizontal component (to the right) and a positive vertical component (upward).
2. The 40 N force points vertically downward. This is a purely vertical component (downward).
3. For the horizontal direction, there is no leftward force to cancel the rightward component of the 25 N force. Thus, the resultant must have a net component to the right.
4. For the vertical direction, the downward force is 40 N. The upward component of the 25 N force is $25 \sin \theta$, which is strictly less than 25 N. Since $40 > 25 > 25 \sin \theta$, the downward force is larger, meaning the net vertical component is downward.
5. A resultant with a rightward horizontal component and a downward vertical component must point downward and to the right. Looking at the options, arrow B matches this direction.

Key Takeaways

• Any force at an angle can be resolved into two perpendicular components (usually horizontal and vertical).
• The resultant force's direction is determined by combining the net horizontal and net vertical components.
• When one component is zero and the other is non-zero, the resultant aligns with the non-zero component; when both are non-zero, the resultant points into the quadrant defined by their signs.

Common Mistakes

• Forgetting to resolve the angled force into components and just guessing based on the larger force (40 N is larger, so one might incorrectly choose C, vertically downward).
• Assuming the resultant must point in the direction of the larger force without considering the horizontal component.
• Confusing the direction of the components (e.g., thinking the 25 N force has a leftward component).

Things to Be Careful About

• Always resolve angled forces into horizontal and vertical components before combining them.
• Remember that a component of a force at an angle is always less than the force itself (e.g., the upward component of 25 N is less than 25 N).
• In multiple-choice questions involving resultants, eliminate options that do not match the signs of the net horizontal and vertical components.