Solution to problem 14.1.15 from the collection of Kepe O.E.

14.1.15 Consider crank 1 with length OA = 0.25 m, which rotates uniformly with angular velocity ? = 10 rad/s. It sets in motion the slide 2, the mass of which is m = 5 kg. It is necessary to determine the module of the main vector of external forces that act on the stage at the moment of time when the angle ? = 60°.

To solve this problem, we apply the law of motion of the rocker: m·a = F - N, where m is the mass of the rocker, a is its acceleration, F is the force acting on the rocker, N is the support reaction force. Since the rocker moves in a horizontal plane, its acceleration is zero, and the equation takes the form: F = N.

The main vector of external forces acting on the stage is the vector F. To determine its module, we use the cosine theorem: F^2 = N^2 + P^2 - 2·N·P·cos?, where P is the vector connecting the points of application N and F, ? - angle between vectors N and P.

Since the crank rotates uniformly, the angle is ? = 60° corresponds to the moment in time when the point of attachment of the link to the crank is at a distance OC = OA·cos? = 0.125 m from the axis of rotation. Then the vector P can be expressed as P = m·g·OS, where g is the acceleration of gravity.

Thus, the module of the main vector of external forces acting on the stage at the moment of time when the angle ? = 60°, equal to: F = N = m g OS = 62.5 N.

Solution to problem 14.1.15 from the collection of Kepe O.?.

This digital product is a solution to mathematical problem 14.1.15, described in the collection “Physics Problem Book for College Students” by author O.?. Kepe. The solution is made in accordance with all the requirements of the task and contains detailed calculations and explanations.

The solution is presented in PDF format and can be used by students and teachers of universities and colleges to prepare for exams, tests and olympiads in physics. It may also be useful for students studying physics at a more advanced level.

By purchasing this digital product, you are guaranteed to get the correct solution to the problem, which will help you better understand physical laws and consolidate your knowledge.

This product is a solution to mathematical problem 14.1.15 from the collection "Physics Problem Book for College Students" by O.?. Kepe.

The problem considers a crank that rotates uniformly with an angular velocity of 10 rad/s and drives a rocker with a mass of 5 kg. It is necessary to determine the module of the main vector of external forces acting on the rocker at the moment of time when the angle of rotation of the crank is 60°.

To solve the problem, the law of motion of the rocker is applied: m·a = F - N, where m is the mass of the rocker, a is its acceleration, F is the force acting on the rocker, N is the support reaction force. Since the rocker moves in a horizontal plane, its acceleration is zero, and the equation takes the form: F = N.

The main vector of external forces acting on the stage is the vector F. To determine its module, the cosine theorem is used: F^2 = N^2 + P^2 - 2·N·P·cos?, where P is the vector connecting the points of application N and F, ? - angle between vectors N and P.

Since the crank rotates uniformly, the angle is ? = 60° corresponds to the moment in time when the point of attachment of the link to the crank is at a distance OC = OA·cos? = 0.125 m from the axis of rotation. Then the vector P can be expressed as P = m·g·OS, where g is the acceleration of gravity.

Thus, the module of the main vector of external forces acting on the rocker at the moment of time when the angle of rotation of the crank is 60° is equal to 62.5 N.

The solution to the problem is presented in PDF format and can be used by students and teachers of universities and colleges to prepare for exams, tests and olympiads in physics.

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The product is the solution to problem 14.1.15 from the collection of Kepe O.?. The problem describes the movement of a crank 0.25 m long with an angular velocity of 10 rad/s, which sets in motion a rocker with a mass of 5 kg. It is necessary to determine the module of the main vector of external forces acting on the rocker at the moment of time when the angle of rotation of the crank is 60°. The solution to the problem allows us to obtain an answer to the question and consists in applying the law of momentum change, taking into account the main vector of external forces. The answer to the problem is 62.5.

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