Solution to problem 14.1.8 from the collection of Kepe O.E.

14.1.8 The center of mass of wheel C moves along a circle of radius R = 1.3 m according to the law s = 4t. Determine the module of the main vector of external forces applied to the wheel if its mass m = 15 kg. (Answer 185)

The problem considers the movement of a wheel in a circle of radius R = 1.3 m. The law of motion of the center of mass of the wheel is given by the equation s = 4t, where s is the coordinate of the center of mass of the wheel, t is time. The mass of the wheel is m = 15 kg. It is necessary to determine the module of the main vector of external forces that act on the wheel.

To solve the problem, we will use the formula for calculating the main vector of external forces: F = ma, where F is the main vector of external forces, m is the mass of the wheel, and is the acceleration of the center of mass of the wheel.

To calculate the acceleration of the center of mass of the wheel, we use the formula for uniform motion in a circle: a = v^2/R, where v is the speed of the center of mass of the wheel.

The speed of the wheel's center of mass can be calculated by taking the derivative of the equation s = 4t: v = ds/dt = 4 m/s.

Now we can calculate the acceleration of the center of mass of the wheel: a = v^2/R = 4^2 / 1.3 = 12.31 m/s^2.

And finally, we can calculate the main vector of external forces: F = ma = 15 * 12.31 = 184.65 N.

Answer: 185 N.

Solution to problem 14.1.8 from the collection of Kepe O.?.

Digital product

Category: Educational materials

Author: Kepe O.?.

Russian language

Format: PDF

Price: 50 rub.

Solution to problem 14.1.8 from the collection of Kepe O.?. is a digital product intended for educational use. The solution to the problem is presented in PDF format, which can be downloaded immediately after purchase.

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Solution to problem 14.1.8 from the collection of Kepe O.?. is a digital product in PDF format intended for educational use. The problem considers the movement of a wheel in a circle of radius R = 1.3 m. The law of motion of the center of mass of the wheel is given by the equation s = 4t, where s is the coordinate of the center of mass of the wheel, t is time. The mass of the wheel is m = 15 kg. It is necessary to determine the module of the main vector of external forces that act on the wheel. To solve the problem, the formula F = ma is used, where F is the main vector of external forces, m is the mass of the wheel, and is the acceleration of the center of mass of the wheel. The acceleration of the center of mass of the wheel is calculated by the formula a = v^2/R, where v is the speed of the center of mass of the wheel, which is calculated as the derivative of the equation s = 4t. The result is the answer: the module of the main vector of external forces acting on the wheel is equal to 185 N. The price for solving the problem is 50 rubles, and after payment the file can be downloaded immediately. Solving the problem can be useful for students and teachers studying physics.

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Problem 14.1.8 from the collection of Kepe O.?. is formulated as follows:

A wheel with a mass m = 15 kg, the center of mass of which moves along a circle of radius R = 1.3 m according to the law s = 4t, is acted upon by external forces. It is required to determine the module of the main vector of external forces.

To solve the problem, it is necessary to use Newton’s second law: the sum of external forces acting on a body is equal to the product of the body’s mass and its acceleration. Since the movement of the center of mass of the wheel along a circle is a uniform movement, its acceleration is directed towards the center of the circle and is equal to v^2/R, where v is the speed of movement of the center of mass of the wheel.

To determine the speed of the center of mass of the wheel, it is necessary to use the expression for the length of the circular arc: s = R * alpha, where alpha is the angle corresponding to the length of the arc s. From the law of motion s = 4t it follows that alpha = 4t/R.

Thus, the speed of the wheel's center of mass is equal to the derivative of the arc length with respect to time: v = ds/dt = 4R.

Using the expression for acceleration and Newton's second law, we get: F = m * v^2/R = m * 4^2 * R/R = 16m.

Substituting the data, we get: F = 16 * 15 = 240 N.

However, the problem requires finding the module of the main vector of external forces, and not their total magnitude. The module of the main vector of external forces is equal to the sum of the modules of these forces.

Since the problem does not indicate exactly what external forces act on the wheel, it is impossible to accurately determine their modules. However, if we assume that only one external force acts on the wheel, then its modulus will be equal to 240 N. If several external forces act on the wheel, then the modulus of the main vector of external forces will be greater than 240 N.

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