Solution to problem 13.3.5 from the collection of Kepe O.E.

A material point M with mass m = 8 kg moves in a horizontal plane along a circle of radius R = 18 m. Need to determine the angle? between force F and speed v at the moment of time when the speed of the point v = 3 m/s, and the tangential acceleration at = 0.5 m/s². The answer is the value of the angle ? in degrees, which is 45.

Solution to problem 13.3.5 from the collection of Kepe O.?.

We present to your attention the solution to problem 13.3.5 from the collection of problems in physics, written by O.?. Kepe. This digital product is intended for those who are studying physics at a more advanced level and want to test their knowledge in solving problems.

The problem is to determine the angle between the force F and the speed v of a material point M with a mass m = 8 kg, moving in a circle of radius R = 18 m in the horizontal plane. To solve the problem, you need to know the speed of the point and the tangential acceleration at the time specified in the condition. The solution to the problem is presented in an easy-to-understand format and provides detailed explanations and solution steps.

By purchasing this digital product, you get access to high-quality material that will help you better understand physical laws and consolidate the knowledge gained. Beautiful design in HTML format will make using this product even more comfortable and enjoyable.

This digital product is a solution to problem 13.3.5 from a collection of physics problems written by O.?. Kepe. The problem requires determining the angle between the force F and the speed v of a material point M with a mass m = 8 kg moving in a circle of radius R = 18 m in the horizontal plane. To solve the problem, you need to know the speed of the point and the tangential acceleration at the time specified in the condition.

The solution to the problem is presented in an easy-to-understand format and provides detailed explanations and solution steps. By purchasing this digital product, you get access to high-quality material that will help you better understand physical laws and consolidate the knowledge gained. Beautiful design in HTML format will make using this product even more comfortable and enjoyable. The answer to the problem is 45 degrees.

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Solution to problem 13.3.5 from the collection of Kepe O.?. consists in determining the angle between the force F and the speed v of the material point M at the moment of time when the speed of the point is 3 m/s and the tangential acceleration is 0.5 m/s².

To solve the problem, it is necessary to use the known formulas of dynamics and kinematics. According to Newton's law, the force F acting on a material point M is equal to the product of its mass and acceleration a, that is, F = ma.

In turn, the acceleration of a material point M can be decomposed into tangential acceleration at and radial acceleration ar, which is equal to v²/R, where v is the speed of the material point, and R is the radius of the circle along which it moves.

Thus, a = at + ar = at + v²/R. From the conditions of the problem it is known that at = 0.5 m/s² and v = 3 m/s. This means ar = v²/R - at = (3² / 18) - 0.5 = 0.5 m/s².

Substituting the values ​​of a and m into the formula F = ma, we obtain the force F acting on the material point M. Then, using the formula for the scalar product of vectors, we can determine the angle between the vectors F and v.

As a result of the calculations, we find that the angle between the force F and the speed v at the moment of time specified in the problem statement is equal to 45 degrees.

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