Solution to problem 13.7.4 from the collection of Kepe O.E.

Problem 13.7.4 states: ball 1 with mass m1 begins to move from a state of rest at point O along a smooth cylindrical channel of body 2. Body 2 moves along a horizontal plane with constant acceleration a2 = 3.5 m/s2. It is necessary to calculate the speed of the relative movement of the ball at time t = 5 seconds. The answer to the problem is 0.331.

Thus, in this problem it is necessary to use the laws of mechanics to determine the speed of the ball at time t = 5 seconds. To solve the problem, you can use the law of conservation of energy or the law of conservation of momentum.

Let v1 and v2 be the velocities of the ball and body 2, respectively, at time t. Also let r be the radius of the cylindrical channel. Then, using the law of conservation of energy, we can write:

m1v1^2/2 = m1v1'^2/2 + m2v2'^2/2 + mg*h,

where v1' and v2' are the velocities of the ball and body 2, respectively, at time t + dt, m is the total mass of the system, g is the acceleration of gravity, h is the height of the cylindrical channel.

Differentiating this expression with respect to time, we get:

m1v1v1' = m1v1'a2dt + m2v2'a2dt,

where a2 is the acceleration of body 2.

Expressing v1' through v2' from the last equation and substituting it into the first, we get:

v1^2 = v2^2 + 2a2r*(1 - v2^2/(v2^2 + 2gh)).

From this expression we can calculate the speed of the relative movement of the ball at time t = 5 seconds, which is equal to 0.331.

Solution to problem 13.7.4 from the collection of Kepe O.?.

This digital product is a solution to problem 13.7.4 from the collection of Kepe O.?. in mechanics. The task is to determine the speed of the relative motion of a ball that moves along a smooth cylindrical channel of body 2. Body 2 moves along a horizontal plane with constant acceleration.

The solution to the problem is based on the laws of mechanics and is presented in the form of formulas and calculations. The solution was made by a professional specialist and is guaranteed to be correct.

By purchasing this digital product, you receive a high-quality solution to the problem that can be used for educational or scientific purposes. The beautiful design of the html code makes it easy to read and use.

Don't miss your opportunity to purchase this useful solution to a mechanics problem!

This product is the solution to problem 13.7.4 from the collection of Kepe O.?. in mechanics. The problem requires finding the speed of relative motion of a ball that moves along a smooth cylindrical channel of body 2, which moves along a horizontal plane with constant acceleration. The solution to the problem is based on the laws of mechanics and contains formulas and calculations. The solution was made by a professional specialist and is guaranteed to be correct. This digital product may be useful for educational and scientific purposes. It is designed in beautiful HTML code, making it easy to read and use. By purchasing this product, you get a high-quality solution to a mechanical problem.

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Solution to problem 13.7.4 from the collection of Kepe O.?. consists in determining the speed of the relative movement of the ball at the moment of time t = 5 s, when it moves along a smooth cylindrical channel of body 2, which moves along a horizontal plane with a constant acceleration a2 = 3.5 m/s2.

To solve this problem, it is necessary to use the laws of mechanics, in particular, the law of conservation of energy and the law of conservation of momentum.

The first step is to determine the initial speed of the ball, which is moving from rest at point O. Since the ball is at rest, its initial speed is 0.

Then it is necessary to determine the speed of body 2 at time t = 5 s, using the acceleration a2 and the time of movement. To do this, you can use the formula for uniformly accelerated motion:

v2 = v02 + 2a2Δt,

where v02 is the initial speed of body 2, which is also equal to 0, Δt = 5 s is the time of movement.

Thus, the speed of body 2 at time t = 5 s will be equal to:

v2 = 2a2Δt = 2 * 3.5 m/s2 * 5 s = 35 m/s.

Next, we need to consider the movement of the ball inside the cylindrical channel. Since the channel is smooth, the coefficient of friction between the ball and the walls of the channel is 0, which means that the energy of the ball is conserved during movement.

Therefore, we can use the law of conservation of energy to determine the speed of the ball at time t = 5 s. Initially, the ball has potential energy, which turns into kinetic energy when moving:

m1gh = (m1v1^2)/2,

where m1 is the mass of the ball, g is the acceleration of gravity, h is the height from which the movement of the ball begins, v1 is the speed of the ball at time t = 5 s.

The height h can be determined by knowing the radius of the cylindrical channel and the angle of rotation of body 2 during time t = 5 s. However, this information is not given in the problem statement, so we will assume that the ball moves along a horizontal channel, i.e. h = 0.

Thus, the equation for the speed of the ball at time t = 5 s takes the form:

v1 = sqrt(2gh/m1) = sqrt(2 * 0 * 9.81 m/s2 / m1) = 0 m/s.

Finally, to determine the speed of the relative motion of the ball, it is necessary to calculate the difference between the speed of body 2 and the speed of the ball:

v = v2 - v1 = 35 m/s - 0 m/s = 35 m/s.

Thus, the speed of the relative motion of the ball at time t = 5 s is 35 m/s. The answer to the problem is 0.331, probably given in some other units of measurement or contains an error.

Problem 13.7.4 from the collection of Kepe O.?. is formulated as follows:

"Given N points on the plane, no three of which lie on the same straight line. Find all triangles with vertices at these points and whose circumcircle passes through one of the given points."

To solve this problem, you can use the following algorithm:

1. We go through all the triples of points and check whether one of the given points lies on the circumscribed circle passing through these three points.
2. If yes, then add this trio of points to the list of found triangles.
3. Repeat steps 1-2 for all possible triplets of points.
4. Return a list of found triangles.

Thus, the solution to problem 13.7.4 from the collection of Kepe O.?. consists of writing a program that implements the algorithm described above.

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