Solution to problem 13.7.1 from the collection of Kepe O.E. 1989

13.7.1. A material point of a locomotive with a mass m = 8·104 kg moves at a speed of 20 m/s along rails laid along the equator from east to west. It is necessary to calculate the modulus of the Coriolis inertial force acting on the locomotive if the angular velocity of the Earth is ω = 0.0000729 rad/s.

To solve the problem, we use the formula for the Coriolis inertia force:

Fк = 2mωv sinα,

where m is the mass of the material point, v is the speed of the point, ω is the angular velocity of the Earth’s rotation, α is the angle between the direction of the point’s speed and the direction to the Earth’s pole.

The speed of the locomotive is directed from east to west, i.e. across the equator, so the angle α between the direction of velocity and the direction to the pole is 90°. Then the formula for the Coriolis force simplifies to:

Fк = 2mωv

Substituting known values, we get:

Fk = 2 * 8·104 * 0.0000729 * 20 = 23.3 N

Thus, the modulus of the Coriolis inertial force acting on a material point of a locomotive weighing 8·104 kg, moving at a speed of 20 m/s along rails laid along the Earth’s equator, at an angular velocity of rotation of the Earth of 0.0000729 rad/s, is equal to 23.3 N.

Solution to problem 13.7.1 from the collection of Kepe O.E. 1989

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In this problem, it is necessary to calculate the modulus of the Coriolis inertial force acting on the material point of a locomotive weighing 8·10^4 kg, moving at a speed of 20 m/s along rails laid along the Earth's equator, at an angular velocity of the Earth's rotation of 0.0000729 rad/s. The solution is presented in the form of formulas and a step-by-step algorithm of actions, which makes it easy to understand the process of solving the problem and apply it in the future in practice.

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Solution to problem 13.7.1 from the collection of Kepe O.E. 1989.

The problem is given about a locomotive with a mass of 8·104 kg moving at a speed of 20 m/s along rails laid along the equator from east to west. It is necessary to determine the modulus of the Coriolis force of inertia of the locomotive, taking into account the angular velocity of the Earth equal to 0.0000729 rad/s. The locomotive is considered a material point.

After payment, you will receive a solution to Kepe problem No. 13.7.1 from a collection of short problems on theoretical mechanics, saved in word format as an image in PNG format, which can be opened on any PC, smartphone or tablet. After checking the solution, we will be grateful if you leave positive feedback.

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