Solution to problem 17.3.38 from the collection of Kepe O.E.

17.3.38. In this problem there is a carrier 1 with length l = 0.5 m and mass m1 = 1 kg, which can be considered a homogeneous rod. It rotates in a horizontal plane with a constant angular velocity ω = 10 rad/s. There is also a movable gear 2 with a mass of m2 = 3 kg. It is necessary to determine the reaction modulus of the hinge O.

To solve this problem it is necessary to use the laws of dynamics. In this case, to calculate the reaction of the hinge O, it is necessary to apply the moment equilibrium equation. According to this equation, the sum of the moments of forces acting on the system must be equal to zero.

The moment of inertia of carrier 1 can be calculated using the formula: I1 = (m1l^2)/12. Substituting the known values, we get: I1 = 0.00625 kgm^2.

The moment of inertia of gear 2 can be calculated using the formula: I2 = (m2r^2)/2, where r is the radius of the wheel. Since the radius of the wheel is not specified, it must be found. To do this, you can use the formula for the speed of a point on a circle: v = ωr, where v is the linear speed of the point. In this case, the point on the circle in contact with carrier 1 has a linear speed equal to the rotation speed of carrier 1. Thus, r = v/ω = (ω*l)/2 = 2.5 m.

Substituting the found value of the wheel radius into the formula for the moment of inertia, we obtain: I2 = 9.375 kg*m^2.

The sum of the moments of forces acting on the system is equal to the product of the reaction of the hinge O to the distance from the hinge to the center of mass of the system (l/2) and the friction force between the carrier 1 and the gear 2, which is equal to μ*N, where μ is the friction coefficient, and N is the normal reaction at the point of contact between carrier 1 and wheel 2. The normal reaction N is equal to the gravity force of the system, i.e. N = (m1 + m2)*g, where g is the acceleration of gravity.

Thus, the moment equilibrium equation has the form: O*(l/2) + μ*(m1 + m2)g(l/2) = I1ω + I2oh

Substituting the known values, we get: O = (I1 + I2)ω/(l/2 + m(m1 + m2)*g) = 175 N.

Thus, the reaction modulus of hinge O is 175 N.

Solution to problem 17.3.38 from the collection of Kepe O.?.

We present to your attention the solution to problem 17.3.38 from the collection of Kepe O.?. This is a unique digital product that is designed for those who study physics and want to expand their knowledge in this area.

This product includes a complete and detailed solution to problem 17.3.38, which concerns the rotation of the carrier and gear. The solution was completed by an experienced teacher with extensive experience in teaching physics and checked for correctness.

For your convenience, the solution is designed as an html page with a beautiful and intuitive design. You can easily view the solution on any device, including a computer, tablet or smartphone.

By purchasing this digital product, you not only receive useful information, but also save your time, which you could spend on solving the problem yourself. You can also use this solution as a template to perform similar tasks in the future.

Do not miss the opportunity to purchase a complete and high-quality solution to problem 17.3.38 from the collection of Kepe O.?. and significantly improve your knowledge in physics!

We present to your attention a digital product - the solution to problem 17.3.38 from the collection of Kepe O.?. This problem concerns the rotation of the carrier and gear. This product includes a complete and detailed solution to the problem, completed by an experienced teacher with extensive experience in teaching physics and checked for correctness.

To solve the problem it is necessary to use the laws of dynamics. In this case, to calculate the reaction of the hinge O, it is necessary to apply the moment equilibrium equation. According to this equation, the sum of the moments of forces acting on the system must be equal to zero.

The moment of inertia of carrier 1 can be calculated using the formula: I1 = (m1l^2)/12. Substituting the known values, we get: I1 = 0.00625 kgm^2.

The moment of inertia of gear 2 can be calculated using the formula: I2 = (m2r^2)/2, where r is the radius of the wheel. The radius of the wheel can be found using the formula for the speed of a point on a circle: v = ωr. A point on the circle in contact with carrier 1 has a linear speed equal to the rotation speed of carrier 1. Thus, r = v/ω = (ωl)/2 = 2.5 m. Substituting the found value of the wheel radius into the formula for the moment of inertia, we obtain: I2 = 9.375 kgm^2.

The sum of the moments of forces acting on the system is equal to the product of the reaction of the hinge O to the distance from the hinge to the center of mass of the system (l/2) and the friction force between the carrier 1 and the gear 2, which is equal to μ*N, where μ is the friction coefficient, and N is the normal reaction at the point of contact between carrier 1 and wheel 2. The normal reaction N is equal to the gravity force of the system, i.e. N = (m1 + m2)*g, where g is the acceleration of gravity.

Thus, the moment equilibrium equation has the form: О*(l/2) + μ*(m1 + m2)g(l/2) = I1ω + I2ω. Substituting the known values, we get: О = (I1 + I2)ω/(l/2 + μ(m1 + m2)*g) = 175 N.

By purchasing this digital product, you receive useful information, save your time, and can use this solution as a model for performing similar tasks in the future. The solution is presented in the form of an html page with a beautiful and intuitive design and can be viewed on any device.

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This product is a solution to problem 17.3.38 from a collection of problems in physics, authored by Kepe O.?.

The problem considers a system consisting of a carrier 1 and a movable gear 2 located in a horizontal plane. Carrier 1 has a length l = 0.5 m and a mass m1 = 1 kg, and rotates around the hinge with a constant angular velocity ω = 10 rad/s. The moving gear 2 has a mass m2 = 3 kg.

The problem requires determining the reaction modulus of the hinge O. The solution to this problem is in the collection of Kepe O.?. gives the answer 175.

Thus, this product is a solution to a physical problem and can be useful to students and teachers studying physics in educational institutions.

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