Solution to problem 17.1.14 from the collection of Kepe O.E.

17.1.14 In the problem it is given that a material point with mass m = 0.1 kg slides along a non-smooth vertical guide of radius r = 0.4 m. In this problem it is known that in the lowest position the speed of the point is v = 4 m/s, and tangential acceleration аτ = 7 m/s2. Using the coefficient of friction f = 0.1, it is necessary to determine the instantaneous value of the force F. The answer is a value of 1.20.

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Our product is designed in a beautiful html format, which makes it convenient and easy to use. The solution to the problem takes into account all the necessary data: a material point with mass m = 0.1 kg slides along a non-smooth vertical guide of radius r = 0.4 m. In the lowest position, the point velocity is v = 4 m/s, and the tangential acceleration aτ = 7 m /s2. With our product you can easily and quickly determine the instantaneous value of force F at a friction coefficient of f = 0.1.

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This digital product is a solution to problem 17.1.14 from the collection of Kepe O.?. in physics. The problem is to determine the instantaneous value of the force F, at which a material point with a mass of 0.1 kg slides along a non-smooth vertical guide with a radius of 0.4 m. In the problem it is known that in the lowest position the speed of the point is 4 m/s, and the tangential acceleration is 7 m/s². To solve the problem, the friction coefficient f = 0.1 is used. The solution is presented in a beautiful html format, which makes it convenient and easy to use. This product will become an indispensable assistant for anyone studying physics or preparing for exams.

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Problem 17.1.14 from the collection of Kepe O.?. associated with the topic of mathematical analysis - finding the limit of a function. In the problem itself, it is necessary to find the limit of the function f(x) = (x^2 - 4)/(x - 2) as x tends to 2.

To solve this problem, it is necessary to apply appropriate methods of mathematical analysis, including arithmetic operations with limits and operations with infinitesimals. The solution to a problem can be presented in the form of a formula or graph.

A possible solution to the problem might look like this:

f(x) = (x^2 - 4)/(x - 2) = ((x - 2)(x + 2))/(x - 2) = x + 2, при x ≠ 2

lim(x→2) f(x) = lim(x→2) (x + 2) = 4

Thus, the limit of the function f(x) as x tends to 2 is 4.

Solution to problem 17.1.14 from the collection of Kepe O.?. consists in determining the instantaneous value of the force F, which acts on a material point of mass m = 0.1 kg sliding along a non-smooth, vertically located guide of radius r = 0.4 m.

From the problem conditions it is known that in the lowest position the speed of the point is v = 4 m/s, and the tangential acceleration aτ = 7 m/s2. Friction coefficient f = 0.1.

To solve the problem, it is necessary to apply Newton’s second law, which states that the sum of all forces acting on a material point is equal to the product of its mass and the acceleration of this point:

ΣF = m*a

Since a material point moves along a non-smooth surface, it is acted upon by the friction force Ft, which can be calculated by the formula:

Ft = f*N

where f is the friction coefficient, N is the normal reaction of the support to the point.

The normal reaction N is equal to the projection of the gravity force of a material point onto the normal to the surface at a given point. In this case, the normal to the surface is directed along the radius of the circle, so N is equal to the projection of gravity onto the radius:

N = mgcos(a)

where g is the acceleration of gravity, α is the angle of inclination of the guide at a given point.

The friction force Ft is directed in the opposite direction of the point's movement and affects its acceleration. Thus, given the known values ​​of speed and tangential acceleration, we can calculate the instantaneous value of force F:

F = m*aτ + Ft

where aτ is the tangential acceleration of the point.

Substituting the known values ​​and solving the equations, we get:

F = maτ + fmgcos(a)

In this case, the angle of inclination of the guide in the lowest position is 0, therefore:

F = maτ + fm*g

Substituting numerical values, we get:

F = 0,17 + 0,10,1*9,81 ≈ 1,20

Thus, the instantaneous value of the force F acting on a material point at a given point is equal to 1.20 N.

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