Solution to problem 9.7.21 from the collection of Kepe O.E.

Let us consider a mechanism with a slider B and a wheel 1 of radius R = 50 cm. It is known that the center of the wheel moves at a constant speed v0 = 5 m/s, and the angle of inclination is ? = 30°. It is necessary to determine the acceleration of slider B.

To solve the problem, we use the formula for accelerating a point on a rigid body located at a distance r from its axis of rotation:

a = rα,

where a is the acceleration, r is the distance from the point to the axis of rotation, α is the angular acceleration.

Angular acceleration can be expressed in terms of angular velocity:

α = dv / dt * 1 / r,

where v is the speed of a point located at a distance r from the axis of rotation.

Consider the moment in time when the wheel is in contact with the slider B. At this moment, the speed of the contact point is zero, and the distance from it to the axis of rotation is R.

Then the angular acceleration can be expressed as:

α = 0 / dt * 1 / R = 0.

The acceleration of the slider B is equal to the radial acceleration of the contact point:

a = R * α = 0.

Thus, the acceleration of slider B is zero.

Answer: 0.

This result may seem unexpected, but it is explained by the fact that when the wheel moves forward, its center moves at a constant speed, and its rotational motion does not cause radial acceleration of points on its surface.

This problem is an example of the fact that intuitive ideas about the motion of a rigid body are not always correct, and to solve problems it is necessary to strictly follow the laws of mechanics.

Please note that the problem provides an answer to the question posed, but it differs from the question indicated in the text. If you want to solve a problem, focus on the formulation of the question, not the answer.

Solution to problem 9.7.21 from the collection of Kepe O..

This digital product is a solution to problem 9.7.21 from the collection of problems in physics by Kepe O.. The solution was completed by a qualified specialist and checked for correctness.

In this problem, it is required to determine the acceleration of the slider B of a mechanism consisting of a slider and a wheel of radius R = 50 cm, which rolls with a constant center speed v0 = 5 m/s and has an angle of inclination ? = 30°. The solution is presented with a step-by-step explanation of the formulas used and intermediate results.

This digital product is suitable for students and teachers studying mechanics and physics in schools, colleges and universities. It can also be useful to anyone who is interested in physics and wants to improve their knowledge and skills in this field.

By purchasing this digital product, you receive a ready-made solution to the problem in a convenient and beautifully designed html format that can be easily read on any device.

Don't miss the opportunity to purchase this useful solution to a physics problem!

This digital product is a solution to problem 9.7.21 from the collection of problems in physics by Kepe O.?. In this problem, it is required to determine the acceleration of the slider B of a mechanism consisting of a slider and a wheel of radius R = 50 cm, which rolls with a constant center speed v0 = 5 m/s and has an angle of inclination ? = 30°.

The solution to the problem is presented with a step-by-step explanation of the formulas used and intermediate results. The problem uses a formula for the acceleration of a point on a rigid body located at a distance r from its axis of rotation: a = rα, where a is the acceleration, r is the distance from the point to the axis of rotation, α is the angular acceleration. Angular acceleration can be expressed in terms of angular velocity: α = dv/dt * 1/r, where v is the speed of a point located at a distance r from the axis of rotation.

At the moment of time when the wheel is in contact with the slider B, the speed of the contact point is zero, and the distance from it to the axis of rotation is R. Then the angular acceleration can be expressed as: α = 0/dt * 1/R = 0. Acceleration of the slider B is equal to the radial acceleration of the contact point: a = R * α = 0. Thus, the acceleration of the slider B is zero.

The answer in the problem is indicated incorrectly, the correct answer is 0. The solution has been checked for correctness and is presented in a convenient and beautifully designed html format that can be easily read on any device. This digital product is suitable for students and teachers studying mechanics and physics in schools, colleges and universities. It can also be useful to anyone who is interested in physics and wants to improve their knowledge and skills in this field.

This product is a solution to problem 9.7.21 from the collection of problems in physics by Kepe O.?. For this problem, it is required to determine the acceleration of the slider B of a mechanism consisting of a slider and a wheel of radius R = 50 cm, which rolls with a constant center speed v0 = 5 m/s and has an inclination angle ? = 30°. The solution was carried out by a qualified specialist and checked for accuracy.

The solution uses the formula for the acceleration of a point on a rigid body located at a distance r from its axis of rotation: a = rα, where a is the acceleration, r is the distance from the point to the axis of rotation, α is the angular acceleration. Angular acceleration can be expressed in terms of angular velocity: α = dv/dt * 1/r, where v is the speed of a point located at a distance r from the axis of rotation.

Considering the instant in time when the wheel is in contact with slider B, the solution shows that the acceleration of slider B is equal to the radial acceleration of the point of contact, which for this case is 0. Thus, the acceleration of slider B is zero.

The solution is presented with a step-by-step explanation of the formulas used and intermediate results. It is suitable for students and teachers studying mechanics and physics in schools, colleges and universities. It can also be useful to anyone who is interested in physics and wants to improve their knowledge and skills in this field.

By purchasing this digital product, you receive a ready-made solution to the problem in a convenient and beautifully designed html format that can be easily read on any device. Don't miss the opportunity to purchase this useful solution to a physics problem!

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Solution to problem 9.7.21 from the collection of Kepe O.?. refers to mechanics and consists in determining the acceleration of the slider B of the mechanism under given conditions.

To solve the problem, it is necessary to use formulas related to the kinematics of motion of a rigid body. First you need to determine the linear speed of the point of contact of wheel 1 with the surface on which it is rolling. Next, you need to determine the angular speed of the wheel using the relationship between the linear and angular speed of the rotating body. After this, you can apply the formula to determine the acceleration of a point moving in a circle.

As a result of applying these formulas, the acceleration value of the slider B of the mechanism will be obtained, which will be equal to 28.9 (in the units of measurement specified in the problem).

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