Solution to problem 17.3.25 from the collection of Kepe O.E.

17.3.25 A homogeneous rod with a length l = 0.6 m begins to rotate in a horizontal plane from a state of rest under the action of a pair of forces with a moment M = 40 N m. It is necessary to find the modulus of the reaction force of the hinge at the initial moment of movement. Answer: 100.

In this problem, we consider a homogeneous rod that begins to rotate in a horizontal plane from a state of rest. To do this, a pair of forces with a moment M = 40 N m acts on the rod. It is necessary to determine the modulus of the reaction force of the hinge at the initial moment of movement. Having solved the problem, we get an answer equal to 100.

Solution to problem 17.3.25 from the collection of Kepe O.?.

This digital product is a solution to problem 17.3.25 from the collection of Kepe O.?. in physics. The solution is presented in easy-to-read HTML format.

The problem considers a homogeneous rod that begins to rotate in a horizontal plane from a state of rest under the action of a pair of forces. It is necessary to determine the modulus of the joint reaction force at the initial moment of movement.

By purchasing this product, you receive a complete and detailed solution to the problem, which will help you better understand physical laws and consolidate the knowledge gained.

This digital product is a solution to problem 17.3.25 from the collection of Kepe O.?. in physics.

The problem considers a homogeneous rod 0.6 m long, which begins to rotate in a horizontal plane from a state of rest under the action of a pair of forces with a moment M = 40 N m. It is necessary to determine the modulus of the joint reaction force at the initial moment of movement.

By purchasing this product, you will receive a complete and detailed solution to the problem, which will help you better understand physical laws and consolidate the knowledge gained. The solution is presented in easy-to-read HTML format. The answer to the problem is 100.

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Solution to problem 17.3.25 from the collection of Kepe O.?. consists in determining the modulus of the hinge reaction force at the initial moment of motion of a homogeneous rod with a length of l = 0.6 m, which begins to rotate in a horizontal plane from a state of rest under the action of a pair of forces with a moment M = 40 N m.

To solve the problem, it is necessary to use the laws of the dynamics of rotational motion of a rigid body. According to the law of conservation of angular momentum, the moment of forces acting on a body is equal to the change in the angular momentum of the body. The law of equilibrium is also applied to determine the reaction of the hinge.

From the problem conditions we know the value of the moment of force M = 40 N m, as well as the length of the rod l = 0.6 m. Thus, we can determine the initial angular velocity of the rod using the formula:

ω₀ = M / I,

where I is the moment of inertia of the rod relative to the axis of rotation, which for a homogeneous rod is equal to I = (1/12) m l², where m is the mass of the rod.

Next, using Newton’s second law for rotational motion, we can determine the joint reaction modulus N:

N = I·α,

where α is the angular acceleration of the rod, which can be determined through the angular velocity and time of rotation of the rod in the first second of movement:

α = ω₀ / t,

where t is the rotation time during the first second of movement.

It is known that during the first second of movement of the rod, its end describes an arc of a circle, the length of which is equal to the length of the rod l. Thus, we can determine the rotation time for the first second of movement:

t = l / v₀,

where v₀ is the linear speed of the end of the rod. Linear speed can be determined through the angular speed and the radius of the circle along which the end of the rod moves:

v₀ = ω₀·r,

where r is the radius of the circle along which the end of the rod moves, equal to l/2.

Thus, the hinge reaction modulus can be determined by the formula:

N = 2·M / l.

Substituting the known values, we get:

N = 2·40 N·m / 0.6 m = 133.33 N.

Answer: 133.

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