Introduction
This problem deals with the Coriolis force, an apparent force experienced by moving objects in a rotating frame such as the Earth. The Coriolis effect is especially significant for high-speed or long-distance movements and is calculated using the formula:
Fc = 2mωv sin(φ)
Where:
- m = mass of the object (in kg)
- ω = angular velocity of Earth = 7.27 × 10⁻⁵ rad/s
- v = velocity of the object (in m/s)
- φ = latitude
Given Data
- Mass of ball, m = 60 g = 0.06 kg
- Speed, v = 50 m/s (moving due south)
- Latitude = 30ºN
- ω = 7.27 × 10⁻⁵ rad/s
- sin(30º) = 0.5
Step-by-Step Calculation
Fc = 2 × 0.06 × 7.27 × 10⁻⁵ × 50 × 0.5
Fc = 2 × 0.06 × 7.27 × 10⁻⁵ × 25
Fc = 0.0002181 N
Direction of Coriolis Force
The Coriolis force always acts perpendicular to the velocity of the object. Since the ball is moving due south at a northern latitude (30ºN), the Coriolis force will act to the right of the motion, which is towards the west.
Final Answer
- Magnitude of Coriolis force: ≈ 0.0002181 N
- Direction: West
Conclusion
The Coriolis force on a ball moving southward at latitude 30ºN is very small in magnitude but plays an important role in large-scale motions like ocean currents, wind patterns, and long-range projectiles. This calculation helps illustrate how Earth’s rotation affects the motion of objects.