b) A ball of mass 60g is moving due south with a speed of 50 ms⁻¹ at latitude 30ºN. Calculate the magnitude and direction of the coriolis force on the ball.

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:

F_c = 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

F_c = 2 × 0.06 × 7.27 × 10⁻⁵ × 50 × 0.5

F_c = 2 × 0.06 × 7.27 × 10⁻⁵ × 25

F_c = 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.