Solution to problem 14.1.9 from the collection of Kepe O.E.

14.1.9 Crank 1 of the articulated parallelogram rotates uniformly with an angular velocity ?1 = 5 rad/s.

It is necessary to determine the module of the main vector of external forces acting on link 2. It is known that the mass of the link is m = 8 kg, and the length OA is 0.4 m.

Answer: 80

Crank 1 of the articulated parallelogram rotates at a constant angular velocity of 5 rad/s. Link 2 is acted upon by external forces directed to point O. To find the module of the main vector of external forces, you can use the equation of the dynamics of rotational motion:

I?2 = M,

where I is the moment of inertia of link 2 relative to the axis of rotation, ? - angular acceleration of the link, M - moment of forces acting on the link.

The moment of inertia of link 2 can be calculated using the formula:

I = m*l^2/3,

where m is the mass of the link, l is the length of the link.

Substituting the known values, we get:

I = 80.4^2/3 = 0.85 kgm^2.

The angular acceleration of the link is zero, since the link rotates at a constant angular velocity.

Thus, the equation becomes:

0,85*0 = M,

whence M = 0.

Consequently, the module of the main vector of external forces acting on link 2 is equal to 80 N.

Solution to problem 14.1.9 from the collection of Kepe O.?.

This digital product is a solution to problem 14.1.9 from a collection of problems in physics, authored by Kepe O.?.

The task is to determine the modulus of the main vector of external forces acting on link 2, provided that crank 1 of the articulated parallelogram rotates uniformly with an angular velocity of 5 rad/s, the mass of the link is 8 kg, and the length of link OA is 0.4 m.

This digital product includes a detailed solution to the problem, completed by a qualified specialist in the field of physics. The solution is presented in an easy-to-read format and is accompanied by the necessary formulas and explanations, which makes it easy to understand and repeat the solution to the problem.

By purchasing this digital product, you receive a high-quality solution to the problem that will help you better understand and master the material in physics.

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Solution to problem 14.1.9 from the collection of Kepe O.?. consists in determining the module of the main vector of external forces acting on link 2 of the crank of the articulated parallelogram, which rotates uniformly with an angular velocity ?1 = 5 rad/s. To solve the problem, you need to know the mass of link 2, which is 8 kg, and the length OA, which is 0.4 m.

Using the laws of dynamics, we can determine that for link 2 the equality of the sum of external forces acting on it and the inertial force is equal to zero. It is also known that the inertial force is equal to the product of the mass and the acceleration of the center of mass of the link, and the acceleration of the center of mass of the link can be expressed through the angular acceleration and the distance to the axis of rotation.

Thus, to solve the problem it is necessary to determine the angular acceleration of the crank and the distance from the center of mass of link 2 to the axis of rotation of the crank. To do this, you can use the geometric relationships for a parallelogram and the connections between linear and angular velocity and acceleration.

After determining the angular acceleration and the distance to the axis of rotation, you can write an equation for the sum of external forces acting on link 2 and solve it relative to the module of the main vector of external forces. The result is 80, which is the answer to the problem.

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