Solution to problem 17.3.30 from the collection of Kepe O.E.

17.3.30. A non-uniform equilateral triangular plate with a mass m = 5 kg rotates in a vertical plane under the action of a pair of forces with a moment M. The angular velocity of the plate is constant and equal to ω = 10 rad/s. It is necessary to determine the modulus of the reaction of the hinge in the position of the plate when this reaction is greatest. Plate size l = 0.3 m. Answer: 136.

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Solution to problem 17.3.30 from the collection of Kepe O.?.

We present to your attention a digital product - a solution to problem 17.3.30 from the collection of Kepe O.?. This product is ideal for students and teachers who are studying physics and want to practice solving mechanical problems.

In this solution you will find a detailed description of the process of solving Problem 17.3.30, which concerns an inhomogeneous equilateral triangular plate, mass 5 kg, rotating in a vertical plane under the action of a pair of forces with a moment M. Using our solution, you will be able to determine the modulus of reaction of the hinge in the position of the plate when this reaction is greatest.

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We present to your attention a digital product - a solution to problem 17.3.30 from the collection of Kepe O.?. This problem concerns a non-uniform equilateral triangular plate with a mass of 5 kg, which rotates in a vertical plane under the action of a pair of forces with a moment M, with a constant angular velocity of 10 rad/s. The task is to determine the modulus of the reaction of the hinge in the position of the plate when this reaction is greatest. The plate size is 0.3 m.

In our solution you will find a detailed description of the process of solving this problem in mechanics. We provide a beautiful html design that allows you to quickly and conveniently familiarize yourself with the material. Our digital product is ideal for students and teachers who are studying physics and want to practice solving problems.

You can purchase our solution to problem 17.3.30 right now and get access to it immediately after payment. Don't miss the opportunity to improve your knowledge and skills in solving mechanical problems with our digital product! The answer to the problem is 136.

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Solution to problem 17.3.30 from the collection of Kepe O.?. is associated with determining the modulus of the reaction of the hinge when it is in the position at which this reaction is greatest. To solve the problem it is necessary to use the laws of mechanics and the equations of rotational motion.

From the problem conditions it is known that a homogeneous equilateral triangular plate with a mass m = 5 kg rotates in a vertical plane under the action of a pair of forces with a moment M and a constant angular velocity ω = 10 rad/s. The plate size is l = 0.3 m.

The first step is to determine the moment of forces acting on the plate. To do this, we use the equation of rotational motion:

М = Iα,

where M is the moment of force, I is the moment of inertia of the plate, α is the angular acceleration.

The moment of inertia of a plate, which has the shape of an equilateral triangle, can be calculated using the formula:

I = (1/6) * m * l^2,

where m is the mass of the plate, l is the length of the side of the equilateral triangle.

We substitute known values:

I = (1/6) * 5 kg * (0.3 m)^2 = 0.225 kg*m^2.

Next, using the formula for the moment of force, we find the moment of a pair of forces:

М = F * r,

where F is the force, r is the radius vector from the axis of rotation to the point of application of the force.

Since the plate rotates in a vertical plane, the moment of force is equal to the vector product of the force and the radius vector:

М = F * l/2,

where l/2 is the distance from the point of application of force to the axis of rotation.

Since the plate rotates at a constant angular velocity, the angular acceleration is zero, and therefore

M = 0.

Thus, the moment of forces acting on the plate is zero. This means that the reaction of the hinge in any position will be equal to the weight of the plate, i.e.

R = m * g = 5 kg * 9.8 m/s^2 = 49 N.

However, in order to find the position at which the hinge reaction is greatest, it is necessary to consider the moments of forces acting on the plate in different positions. For example, if the plate is in a vertical position, then the hinge reaction moment will be zero, and the hinge reaction will be equal to the weight of the plate. If the plate is in a horizontal position, then the reaction of the hinge will be equal to twice the weight of the plate, i.e.

R = 2 * m * g = 98 Н.

Thus, in order to find the position at which the hinge reaction is greatest, it is necessary to consider the moments of forces at various positions of the plate. However, the answer to the problem is already given in the condition and is equal to 136 N, which may mean that another problem is being solved or an inaccurate description of the condition is given. If there is a more precise description of the problem, then you can consider it and give a more accurate answer.

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