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QExample - 3: HC Verma: Concepts of Physics - Volume 1 Physics and Mathematics Example - 3 Solution: A force of 10.5 N acts on a particle along a direction making…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the angle reference, applying sine instead of cosine when the angle is measured from the vertical axis. Always align the trigonometric function with the axis of the given angle: use cosine for the component along the axis and sine for the perpendicular component.

A force of 10.5 N acts on a particle along a direction making an angle of 37° with the vertical. Find the component of the force in the vertical direction.

Step-by-Step Verified Solution

Given:

  • Magnitude of the force (F) = 10.5 N
  • Angle between the force and the vertical direction (θ) = 37°

To Find:

  • The vertical component of the force (F_vertical)

Concept:

The vertical component of the force can be found using the cosine of the angle between the force and the vertical direction.

Formula:

F_vertical = F * cos(θ)

Calculation:

  1. Substitute the given values into the formula:
  2. F_vertical = 10.5 N * cos(37°)
  3. We know that cos(37°) ≈ 0.8 (or 4/5). Substitute this value:
  4. F_vertical = 10.5 N * 0.8
  5. Calculate the result:
  6. F_vertical = 8.4 N

Answer:

The component of the force in the vertical direction is 8.4 N.

All Questions in this Chapter

QExample - 1 QExample - 2 QExample - 3 QExample - 4 QExample - 5 QExample - 6 QExample - 7

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