15.7.10. Let's assume that there are two identical blocks 1 and 2, which have mass m1 = m2 and radii R1 = R2. They are homogeneous disks and begin to move from a state of rest under the influence of gravity. We need to determine the speed of the center C of block I after it has descended to a distance s = 1 m.
To solve this problem, you can use the laws of conservation of energy and angular momentum. Since the initial speed of the blocks is zero, their initial kinetic energy is also zero. When block I descends to a distance s = 1 m, its potential energy will decrease by m1gs, where g is the acceleration of gravity. This potential energy will turn into the kinetic energy of block I, as well as block II.
Thus, we can write the equation for the law of conservation of energy:
m1gs = (m1+m2)v^2/2,
where v is the speed of center C of block I after it has descended a distance s.
The law of conservation of angular momentum tells us that the angular momentum of a pulley system must be conserved during movement. Since the blocks have the same radii, their moments of inertia will also be equal. Thus, we can write the equation for the law of conservation of angular momentum:
m1vs = (m1+m2)v,
where vs is the initial speed of the block system.
Solving these two equations for v, we get:
v = sqrt(2m1gs/(m1+m2)).
Substituting numerical values, we get:
v = sqrt(29.811/(2*1)) = 2.37 m/s.
Thus, the speed of the center C of block I after it has descended to a distance s = 1 m is equal to 2.37 m/s.
This digital product is the solution to problem 15.7.10 from the collection of problems in physics by Kepe O.?. This problem concerns the motion of two homogeneous disks starting to move from a state of rest under the influence of gravity. Solving this problem will help pupils and students learn the laws of conservation of energy and angular momentum, as well as understand the movement of bodies.
The solution to the problem is presented in PDF format and describes in detail all stages of the solution. It will be useful both for independent work and for use in physics lessons.
When you purchase this digital product, you can be sure that you will receive a quality product that will help you understand a difficult physics problem.
After purchase, you can download the file and use it as a study guide to prepare for exams or to study physics on your own. The solution to the problem can also be used by physics teachers as material for lessons.
This product is a solution to problem 15.7.10 from the collection of problems in physics by Kepe O.?. The problem concerns the motion of two identical disk blocks starting to move from rest under the influence of gravity, and requires determining the speed of the center of block I after lowering to a distance s = 1 m. The solution to the problem is based on the laws of conservation of energy and angular momentum.
This digital product is presented in PDF format, contains 2 pages, is written in Russian and describes in detail all stages of the solution. It can be used as a study guide for preparing for exams or for self-studying physics. The solution to the problem can also be used by physics teachers as material for lessons.
When you purchase this digital product, you can be sure that you will receive a quality product that will help you understand a difficult physics problem. After purchasing, you can download the file and use it as you wish.
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The product is the solution to problem 15.7.10 from the collection of Kepe O.?. The problem is to determine the speed of the center of block I after it has dropped down a distance s = 1 m. This block is a homogeneous disk of mass m1 and radius R1, which is in an initial state of rest. The second block, designated as block II, is also a homogeneous disk with mass m2 and radius R2, and begins to move from rest under the influence of gravity at the same time as block I. In this case, the masses of blocks I and II are equal, and the radii are also equal to each other.
To solve the problem, it is necessary to use the laws of mechanics, namely the law of conservation of energy and the law of conservation of momentum. After carrying out the necessary calculations, the answer to the problem was equal to 2.37.
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