Solution to problem 15.6.8 from the collection of Kepe O.E.

This problem considers the movement of a thin-walled cylinder of mass m and radius R = 0.5 m without sliding along a horizontal plane. The initial angular velocity of the cylinder is ?0 = 4 rad/s, and the rolling friction coefficient is ? = 0.01 m.

It is necessary to determine the path traveled by the center C of the cylinder until it stops.

Solution: First, let's determine the acceleration of the center of mass of the cylinder. Since the cylinder rolls without sliding, the acceleration of the center of mass will be equal to the angular acceleration multiplied by the radius of the cylinder: a = R * ?'' = R * ?' * ? = 0.5 * 4 = 2 m/s^2.

Then we determine the rolling friction force acting on the cylinder. To do this, we use the formula: Ftr = ? *m*g,

where m is the mass of the cylinder, g is the acceleration of gravity, ? - rolling friction coefficient. Ftr = 0.01 * m * 9.81 = 0.0981m N.

Since the cylinder rolls without sliding, the work done by the rolling friction force is equal to the work done by gravity. Thus, we can write an equation to determine the path traveled by the center C of the cylinder before stopping: m * g * h = Ftr * s,

where h is the height to which the center of mass of the cylinder rises before stopping, s is the path traveled by the center C of the cylinder before stopping. h = v0^2 / (2 * a) = 8 / 4 = 2 m. s = h / sin(?) = 2 / sin(arctg(2 / 20)) = 20.4 m.

Thus, the distance traveled by the center C of the cylinder to the stop is 20.4 m.

Solution to problem 15.6.8 from the collection of Kepe O.?.

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Format: PDF

Russian language

File size: 1 MB

Price: 100 rubles

The offered product is a solution to problem 15.6.8 from the collection of Kepe O.?. in physics. The problem considers the motion of a thin-walled cylinder of mass m and radius R = 0.5 m without sliding along a horizontal plane. The problem is to determine the path traveled by the center C of the cylinder to stop at the initial angular velocity of the cylinder ?0 = 4 rad/s and the rolling friction coefficient ? = 0.01 m.

In solving the problem, the acceleration of the center of mass of the cylinder is first determined, which is equal to the angular acceleration multiplied by the radius of the cylinder. The rolling friction force acting on the cylinder is then determined using Eq. Next, using the law of conservation of energy, an equation is written to determine the path traveled by the center C of the cylinder to stop. The solution is presented in PDF format, which makes it easy to read on a computer or mobile device, and is sold for a price of 100 rubles. This product can be useful for students and teachers who are interested in physics and mechanics, and will help them successfully solve such problems and get high grades in their studies.

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Solution to problem 15.6.8 from the collection of Kepe O.?. consists in determining the path traveled by the center of a thin-walled cylinder before stopping on a horizontal plane under given initial conditions. To do this, it is necessary to apply the laws of mechanics, namely, the equation of motion of a rigid body without sliding and the equation of energy.

From the equation of motion it follows that when moving without sliding, the angular velocity of the cylinder is maintained, and its center moves at a constant speed. Using the energy equation, we can express the speed of the center of the cylinder at the moment of stopping. Then, knowing the time of movement before stopping, you can find the path traveled by the center of the cylinder.

The coefficient of rolling friction between the cylinder and the horizontal plane is taken into account in the equation of motion, and to use it, knowledge of the formula for the moment of inertia of a thin-walled cylinder is necessary.

The answer to the problem is 20.4 meters.

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