Solution to problem 8.4.11 from the collection of Kepe O.E.

8.4.11 Load acceleration calculation Given: the angular velocity of gear 1 changes according to the law ?1 = 2t², gear radii R₁ = 1 m, R₂ = 0.8 m and the radius of the drum r = 0.4 m. It is required to determine the acceleration of load 3 at time t = 2 s. Answer: The angular speed of wheel 1 is related to the angular speed of wheel 2 by the relation: ?2 = R1/R2 * ?1 = 1.25 * ?1 = 2.5t² (1) The angular speed of the drum is related to the angular speed of wheel 2 by the relation: ?2 = r/R2 * ?3 => ?3 = R2/r * ?2 = 3.125 * ?2 = 7.8125t² (2) Differentiating equation (2) with respect to time, we find the acceleration of the load: a = d?3/dt = 15.625t[m/s²] (3) Substituting t = 2 s into equation (3), we obtain: a = 31.25 [m/s²] Answer: 4. Thus, the acceleration of load 3 at time t = 2 s is equal to 31.25 m/s².

Solution to problem 8.4.11 from the collection of Kepe O.?.

This digital product is a solution to problem 8.4.11 from a collection of physics problems for students and secondary school students, authored by O.?. Kepe. The solution to this problem is presented in the form of a detailed description of the solution algorithm, with a step-by-step explanation of the initial data and calculations, as well as an answer to the question posed.

Problem 8.4.11 is to calculate the acceleration of the load at time t = 2 s, provided that the angular velocity of gear 1 changes according to the law ?1 = 2t², gear radii R₁ = 1 m, R₂ = 0.8 m and drum radius r = 0.4 m.

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The digital product you are purchasing is a solution to problem 8.4.11 from the collection of physics problems for undergraduates and secondary school students, authored by O.?. Kepe. In this problem, it is necessary to find the acceleration of load 3 at time t = 2 s, provided that the angular velocity of gear 1 changes according to the law ?1 = 2t2, gear radii R1 = 1 m, R2 = 0.8 m and drum radius r = 0.4 m.

The solution to the problem consists of the following steps. First, it is necessary to express the angular speeds of wheel 2 and load 3 through the angular speed of wheel 1, using the relationship between the radii of the gears and the drum. Then, by differentiating the equation for the angular velocity of load 3 with respect to time, we can find the acceleration of the load at time t = 2 s.

The answer to the question posed is 31.25 m/s2. This digital product can be useful for students and secondary school students studying physics, as well as teachers for preparing for lessons and tests.

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The proposed product offer is a solution to problem 8.4.11 from the collection of Kepe O.?. The task is to determine the acceleration of load 3 at time t = 2 s when the angular velocity of gear 1 changes according to the law ?1 = 2t2, provided that the gear radii R1 = 1 m, R2 = 0.8 m and the drum radius r = 0.4 m. The answer to the problem is 4.

To obtain a solution to the problem, you need to apply the appropriate equations to determine the angular acceleration and convert it into the linear acceleration of load 3. Then you need to substitute the known values ​​into the equation and calculate the answer. The solution to this problem can be useful for students and teachers studying the course of solid body mechanics and dynamics.

Solution to problem 8.4.11 from the collection of Kepe O.?. is as follows:

Given a function f(x) = x^3 - 6x^2 + 9x + 7. It is necessary to find all extremum points of this function and determine whether they are minimum or maximum points.

To solve the problem, you need to find the derivative of the function f(x) and equate it to zero in order to find the points where the derivative is equal to zero. Next, you need to find the value of the second derivative of the function at the found points. If the second derivative is greater than zero, then the found point is a minimum point, but if it is less than zero, then the point is a maximum point.

Having calculated the derivative of the function f(x) and equating it to zero, we get the equation 3x^2 - 12x + 9 = 0. Solving this equation, we get two extremum points: x1 = 1 and x2 = 3.

Next, you need to calculate the second derivative of the function f(x) and determine its sign at points x1 and x2. Having calculated the second derivative, we obtain the equation 6x - 12. Substituting the found points x1 and x2 into this equation, we obtain the following values: f''(1) = -6 and f''(3) = 6.

Based on the values ​​of the second derivative, we can conclude that point x1 = 1 is the maximum point of the function f(x), and point x2 = 3 is the minimum point of the function f(x).

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