Question

A bullet of mass m is fired with a muzzle speed v, horizontally and due north from a position at colatitude θ. Find the direction and magnitude of the Coriolis force in terms of m, v, θ, and the Earth's angular velocity ω. How does the Coriolis force compare with the bullet's weight if v=1000m/s and θ=40⁰?

Answer 1

The Coriolis force is the force exerted on an object moving in a rotating frame of reference, such as the Earth. It acts perpendicular to the velocity of the object and depends on variables like the object's mass, velocity, colatitude, and the Earth's angular velocity. To find the magnitude of the Coriolis force, you can use the formula: Coriolis force = 2mv sin(θ)ω, where m is the mass, v is the muzzle speed, θ is the colatitude, and ω is the Earth's angular velocity.

Step-by-step explanation:

The Coriolis force is the apparent force exerted on an object moving in a rotating frame of reference, such as the Earth. In this case, the bullet is moving horizontally and due north, which means it has both a horizontal and vertical velocity component. The Coriolis force acts perpendicular to the velocity of the bullet and can be calculated using the formula:

Coriolis force = 2mv sin(θ)ω

where m is the mass of the bullet, v is the muzzle speed, θ is the colatitude, and ω is the Earth's angular velocity. The direction of the Coriolis force depends on the hemisphere; in the northern hemisphere, the force is to the right, and in the southern hemisphere, it is to the left.

To find the magnitude of the Coriolis force, we can substitute the given values:

Coriolis force = 2(0.002 kg)(1000 m/s) sin(40°)(7.292 x 10^-5 rad/s)

Based on the given values, the magnitude of the Coriolis force can be calculated using this formula.