Solution to problem 13.3.18 from the collection of Kepe O.E.

13.3.18 The mass of a material point is equal to m = 16 kg. It moves in a plane along a curved path under the action of the resultant force F = 0,3t. It is necessary to determine the speed of a point at a time t = 20 s when the radius of curvature of the trajectory ? = 12 m, and the angle between the force and velocity vectors is a = 50°. Round the answer to two decimal places (Answer 1.86).

Solution: Let's create an equation for Newton's second law for this system: F = ma F = mv²/R Where v - point speed, R - radius of curvature of the trajectory. The angle between the force and velocity vectors can be determined by the formula: cos(a) = (F·v)/(|F|·|v|) Since the resultant force is directed along the trajectory, it coincides with the tangent to the trajectory and is perpendicular to the radius of curvature. Therefore, we can write: F·v = |F|·|v|·sin(a) Substitute the resulting expressions for force and angle into the equation for force: mv²/R = |F|·|v|·sin(a) v = (√(|F|·R·sin(a)))/√(m) Let's substitute the known values: F = 0,3t = 0.3·20 = 6 N R = 12 m m = 16 kg a = 50° Then: v = (√(|6·12·sin(50°)|))/√(16) ≈ 1.86 m/s Answer: 1.86.

Solution to problem 13.3.18 from the collection of Kepe O.?.

We present to your attention a digital product - a solution to problem 13.3.18 from the collection of Kepe O.?. This product will be useful for students who are studying mechanics and need additional materials to independently study the topic.

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Don't miss the opportunity to purchase our digital product and greatly simplify the process of learning mechanics!

We present to your attention a digital product - a solution to problem 13.3.18 from the collection of Kepe O.?. This product is intended for students studying mechanics and who need additional materials for independent study of the topic.

When purchasing a digital product, you will receive a ready-made solution to problem 13.3.18, which includes a detailed description of all stages of the solution, as well as the final answer. All material is presented in a beautiful html format, which ensures convenient and enjoyable reading.

For this problem, we compiled the equation of Newton's second law, where F is the resultant force, m is the mass of the material point, v is the speed of the point, R is the radius of curvature of the trajectory. We also used a formula to determine the angle between the force and velocity vectors, and also took into account that the resultant force is directed along the trajectory and coincides with the tangent to the trajectory.

Substituting known values ​​(mass, resultant force, radius of curvature of the trajectory and the angle between the force and velocity vectors) into the equation for speed, we received the answer to the problem: the speed of the point at time t = 20 s is approximately 1.86 m/s. The answer was rounded to two decimal places, as required in the task conditions.

Our team consists of experienced specialists in the field of mathematics and physics who guarantee high quality of the product. We are also available to answer any questions you may have and provide additional information upon request. Don't miss the opportunity to purchase our digital product and greatly simplify the process of learning mechanics!

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Problem 13.3.18 from the collection of Kepe O.?. relates to the topic of function optimization. To solve the problem, it is necessary to find the minimum of a function of two variables with restrictions. The conditions of the problem indicate the initial approximation and the permissible range of changes in the variables.

To solve the problem, you can use various optimization methods, for example, the penalty function method or the steepest descent method. Ultimately, the solution to the problem represents the values ​​of the variables at which the minimum of the function is achieved, satisfying the restrictions.

The solution to this problem can be useful for students and professionals involved in mathematical modeling and optimization of functions, as well as for solving practical problems in various fields, for example, in economics, physics, engineering, etc.

Problem 13.3.18 from the collection of Kepe O.?. is formulated as follows:

A material point with mass m = 16 kg moves in a plane along a curved path under the action of a resultant force F = 0.3t. It is necessary to determine the speed of a point at the time t = 20s, when the radius of curvature of the trajectory is ? = 12 m and the angle between the force and velocity vectors a = 50°. The answer to the problem is 1.86.

To solve the problem, you can use the law of conservation of energy and the law of change in momentum. From the conditions of the problem, the resultant force F is known, which acts on the point and changes its speed. The radius of curvature of the trajectory and the angle between the force and velocity vectors make it possible to determine the direction and magnitude of the centripetal acceleration of the point. Knowing the centripetal acceleration, you can determine the speed of the point at time t = 20s using the formula for centripetal acceleration and the law of conservation of energy.

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