Zhukovsky's bench with a man standing in the center of it and

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A Zhukovsky bench with a person standing in the center of it and leaning on a crowbar 1.2 m long and weighing 12 kg is rotated by the tension of the cord F = 20 N, acting for t = 7 s on a pulley R = 15 cm. Moment of inertia of the bench with a person J=10 kg*m^2. It is necessary to determine the frequency of rotation of the bench after the person lifts the crowbar to his chest, turning it horizontally and holding on to its middle. Solution to the problem: Initially, it is necessary to determine the moment of force acting on the pulley: Ft = F ⋅ R = 20 N ⋅ 0.15 m = 3 N⋅m Then we calculate the moment of inertia of the bench-man-crowbar system: J = Jsc + Jch + Jl = 10 kg⋅m² + 80 kg⋅m² + 0.1 kg⋅(1.2 m / 2)² = 90.04 kg⋅m² where Jsk is the moment of inertia of the bench, Jch is the moment of inertia of a person, Jl is the moment of inertia of the crowbar. When a person lifts the crowbar onto his chest, the moment of inertia of the system will change. Let's calculate it: J' = Jsk + Jch + Jl' = 10 kg⋅m² + 80 kg⋅m² + 0.1 kg⋅(0.6 m)² = 49.24 kg⋅m² where Jl' is the moment of inertia of the scrap after lifting to the chest. To determine the angular velocity of the system, we use the law of conservation of angular momentum: Jω = J'ω' + L where ω is the angular velocity of the system before lifting the scrap, ω' is the angular velocity of the system after lifting the scrap, L is the angular momentum of the system before lifting the scrap. At the initial moment of time, the angular momentum of the system is equal to: L = Jω = 90.04 kg⋅m² ⋅ ω After lifting the crowbar, the angular momentum of the system is also conserved. This means that J'ω' = L or ω' = Jω / J' = (90.04 kg⋅m² ⋅ ω) / 49.24 kg⋅m² = 1.83 ω Thus, the angular velocity of the system after lifting the scrap will be in 1.83 times more than before the rise. The bench rotation frequency can be calculated using the formula: ω' = 2πf' where f' is the bench rotation frequency after lifting the crowbar. Then f' = ω' / 2π = (1.83 ω) / (2π) = 0.29 ω Answer: the rotational speed of the bench after lifting the crowbar will be 0.29 angular speed, which increased by 1.83 times after lifting the crowbar . To solve the problem, the laws of conservation of angular momentum and formulas for calculating the moment of inertia and angular velocity were used. The moment of force acting on the pulley was calculated as the product of the force and the radius of the pulley. After lifting the crowbar to the chest, the moment of inertia of the system changed, so the corresponding formula was used to calculate the new moment of inertia. We are pleased to present you our digital product - a unique product “Zhukovsky Bench”. This is an interesting problem for lovers of physics and mathematics, which can be solved independently or used for teaching. The problem presents data on a Zhukovsky bench with a person standing in its center and leaning on a crowbar 1.2 m long and weighing 12 kg. With the help of a cord tension F = 20 N, acting for t = 7 s on a pulley R = 15 cm, the bench was rotated. The moment of inertia of a bench with a person is J=10 kg*m^2. After this, the task asks to determine the rotation frequency of the bench after a person lifts the crowbar onto his chest, turning it horizontally and holding on to its middle. IN In our digital goods store, we offer only high-quality products that are made in compliance with all requirements and standards. This product is equipped with a beautiful html design that will allow you to easily and quickly familiarize yourself with the condition of the problem and its solution. By purchasing our digital product "Zhukovsky Bench", you get access to a detailed solution to the problem with a brief record of the conditions, formulas and laws used in the solution, derivation of the calculation formula and the answer. If you have any questions regarding the solution, our team will help you resolve them. Don't miss the opportunity to purchase our interesting and useful digital product "Zhukovsky's Bench" directly

The Zhukovsky bench with a man standing in its center is a physical system that was set into rotation by a tension cord with a force F=20 N, acting for a time t=7 s on a pulley R=15 cm. The moment of inertia of the bench with a man J =10 kg*m^2. At the initial moment of time, the bench rotated with a certain angular velocity ω, which is unknown. Next, a person lifts a crowbar 1.2 m long and weighs 12 kg onto his chest, turning it horizontally and holding on to its middle. After this, it is necessary to determine the rotation frequency of the bench. To solve the problem, it is necessary to use the law of conservation of angular momentum, which allows us to establish a connection between the angular velocity of the system before and after lifting the crowbar onto the chest. In this case, the moment of inertia of the system will change, since the location of the masses in the system will change. The new moment of inertia of the system can be calculated using the formula J' = Jsk + Jch + Jl', where Jsk is the moment of inertia of the bench, Jch is the moment of inertia of a person, Jl' is the moment of inertia of the crowbar after lifting to the chest. The angular velocity of the system after lifting the crowbar can then be calculated using the law of conservation of angular momentum: Jω = J'ω' + L, where L is the angular momentum of the system before lifting the crowbar. From this relationship we can express the angular velocity after lifting the crowbar, and then the rotation frequency of the bench. As a result, the rotation frequency of the bench after lifting the crowbar will be 0.29 angular velocity, which increased by 1.83 times after lifting the crowbar. In our digital product "Zhukovsky's Bench" you will find a detailed solution to the problem with a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. If you have any questions regarding the solution, our team will help you resolve them.

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The Zhukovsky bench is a sports equipment designed for performing abdominal and core exercises. This bench is designed to allow a person to stand in the center and perform exercises using a crowbar that is 1.2 m long and weighs 12 kg. To cause the bench to rotate, it is necessary to apply a cord tension with a force of 20 N acting on a pulley with a radius of 15 cm for 7 seconds. The moment of inertia of a bench with a person is 10 kg*m^2.

To determine the speed of rotation of the bench after a person lifts the crowbar onto his chest, turning it horizontally and holding on to its middle, the following formula must be used:

ω = (F * R * t) / (J + m * R^2)

where ω is the desired rotation frequency, F is the tension force of the cord, R is the radius of the pulley, t is the time of action of the force, J is the moment of inertia of the bench with a person, m is the mass of the crowbar.

Substituting the known values, we get:

ω = (20 N * 0.15 m * 7 s) / (10 kg*m^2 + 12 kg * (0.6 m)^2) ≈ 0.25 rad/s

Thus, the rotation frequency of the bench after lifting the crowbar is approximately 0.25 rad/s.

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