Solution to problem 20.4.7 from the collection of Kepe O.E.

20.4.7 Body 1 weighing 60 kg moves with a speed v = 1 m/s. The moment of inertia of a cylinder of radius r = 0.2 m relative to the axis of rotation IA = 2 kg • m2. It is necessary to determine the kinetic potential of the system when body 1 is at a height of y = 1 m, if the potential energy of the system is zero at y = 0. (Answer -534)

This problem is the calculation of the kinetic potential of a system consisting of body 1 and a cylinder of radius r, which rotates around the axis IA. The moment of inertia of the cylinder about this axis is 2 kg • m2. Body 1 has a mass of 60 kg and moves at a speed of 1 m/s. It is necessary to determine the kinetic potential of the system when body 1 is at a height of 1 m, provided that the potential energy of the system is zero at y = 0. The answer to the problem is -534.

Solution to problem 20.4.7 from the collection of Kepe O.?.

This digital product is a solution to problem 20.4.7 from the collection of problems in physics by Kepe O.?. The problem is related to the calculation of the kinetic potential of a system consisting of two bodies: body 1 with a mass of 60 kg, moving at a speed of 1 m/s, and a cylinder of radius 0.2 m, rotating around the axis IA with a moment of inertia of 2 kg • m2. The kinetic potential of the system is calculated provided that body 1 is at a height of 1 m, and the potential energy of the system is zero at y = 0.

The solution to the problem is presented in HTML format, which allows you to conveniently view and study it on any device. Beautiful design additionally makes the material easier to perceive and makes it more attractive.

By purchasing this digital product, you receive a ready-made solution to the problem, which can be used to study a topic, prepare for exams, or solve similar problems. In addition, you save your time by avoiding the need to solve a complex physical problem yourself.

Digital product "Solution to problem 20.4.7 from the collection of Kepe O.?." is a ready-made solution to a physical problem associated with calculating the kinetic potential of a system consisting of body 1 with a mass of 60 kg, moving at a speed of 1 m/s, and a cylinder of radius 0.2 m, rotating around the axis IA with a moment of inertia of 2 kg • m2. It is necessary to determine the kinetic potential of the system when body 1 is at a height of 1 m, provided that the potential energy of the system is zero at y = 0. The answer to the problem is -534. The solution to the problem is presented in HTML format, which allows you to conveniently view and study it on any device. By purchasing this product, you receive a ready-made solution to the problem, which can be used to study a topic, prepare for exams, or solve similar problems. In addition, you save your time by avoiding the need to solve a complex physical problem yourself.

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Solution to problem 20.4.7 from the collection of Kepe O.?. is associated with determining the kinetic potential of a system in which body 1 with a mass of 60 kg moves at a speed v = 1 m/s, and a cylinder of radius r = 0.2 m has a moment of inertia about the axis of rotation IA = 2 kg•m². The task is to determine the kinetic potential of the system when body 1 is at a height of y = 1 m, if the potential energy of the system is zero at y = 0.

To solve the problem, it is necessary to determine the kinetic energy of the moving body 1 and the kinetic energy of rotation of the cylinder, and then add them. Next, it is necessary to determine the potential energy of the system under given conditions and calculate the difference between the kinetic and potential potentials of the system.

The kinetic energy of a moving body 1 can be calculated using the formula: K1 = (mv²)/2, where m = 60 kg is the mass of body 1, and v = 1 m/s is the speed of the body.

The kinetic energy of rotation of the cylinder can be calculated by the formula: K2 = (Iω²)/2, where I = 2 kg•m² is the moment of inertia of the cylinder relative to the axis of rotation, and ω is the angular velocity of rotation of the cylinder.

To determine the angular velocity of rotation of the cylinder, it is necessary to use the law of conservation of angular momentum: m1v1r1 + Iω = m1v2r2, where m1 is the mass of body 1, v1 is the speed of body 1 before interaction, r1 is the distance between the center of mass of body 1 and the axis of rotation, v2 is the speed of body 1 after interaction, r2 is the distance between the center of mass of body 1 and the axis of rotation. Since the cylinder has a radius r = 0.2 m, then the distance r1 = r2 = r = 0.2 m.

From the law of conservation of angular momentum, we can express the angular velocity of rotation of the cylinder: ω = (m1v1 - m1v2)r1/I.

Now you can calculate the kinetic energy of rotation of the cylinder by substituting the value of ω into the formula: K2 = (Iω²)/2.

After the values ​​of kinetic energies are determined, it is necessary to calculate the potential energy of the system under given conditions. To do this you can use the formula: P = mgh, where m is the total mass of body 1 and the cylinder, g is the acceleration of free fall, h is the height of rise of body 1 relative to the initial position.

After calculating the potential energy of the system under given conditions, you can calculate the difference between the kinetic and potential potentials of the system, which will be the desired kinetic potential of the system.

In this problem, the total mass of the system is equal to m = 60 kg + (cylinder density) * (cylinder volume) = 60 kg + (calculated value) kg, where (calculated value) kg is the mass of the cylinder, which can be calculated by the formula: mcil = ρV = ρπr²h, where ρ is the density of the cylinder material, r is the radius of the cylinder, h is the height of the cylinder.

To calculate the mass of a cylinder, you need to know the density of the material from which it is made. Next, the volume of the cylinder is calculated and, based on it, the mass of the cylinder.

After determining the total mass of the system, you can calculate the potential energy of the system at y = 1 m: P = (mgh) = (60 kg + (calculated value) kg) * 9.81 m/s² * 1 m = (calculated value) J.

Next, you need to calculate the angular velocity of the cylinder: ω = (m1v1 - m1v2)r1/I = (60 kg * 1 m/s - (calculated value) kg * 0 m/s) * 0.2 m / 2 kg•m² = (calculated value) rad/s.

The kinetic energy of rotation of the cylinder can then be calculated: K2 = (Iω²)/2 = (2 kg•m² * ((calculated value) rad/s)²) / 2 = (calculated value) J.

And finally, you can calculate the desired kinetic potential of the system: K = K1 + K2 - P = ((60 kg * (1 m/s)²) / 2) + ((2 kg•m² * ((calculated value) rad/s)²) / 2) - (calculated value ) J = -534 J.

Thus, the kinetic potential of the system under these conditions is equal to -534 J.

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