Solution of problem 1.2.15 from the collection of Kepe O.E.

Solution to problem 1.2.15 from the collection of Kepe O..

This product is a solution to problem 1.2.15 from a collection of physics problems for students and secondary school students, authored by Kepe O..

The problem is to determine the pressure that a uniform ball weighing 12 N exerts on a smooth inclined plane at an inclination angle of 60 degrees. The solution to this problem is presented in text form with a step-by-step explanation of each stage of the solution.

This digital product is intended for those who study physics and want to improve their knowledge in this area. Solving problem 1.2.15 from the collection of Kepe O.. will allow you to understand the technique of solving physical problems and get additional practice in solving them.

By purchasing this product, you get access to a text file with the solution to problem 1.2.15 in PDF format, which you can save on your computer or print.

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Solution to problem 1.2.15 from the collection of Kepe O.?. consists in determining the pressure of a ball on a smooth inclined plane, provided that the ball is held by a rope at an angle of inclination of 60 degrees.

To solve the problem, it is necessary to use the law of conservation of energy, which states that the mechanical energy of a system remains constant at all its points unless external forces act on it.

In this problem, we can write an equation for the mechanical energy of a system consisting of a ball and the earth. In this case, the potential energy of a ball located at a height h above the ground is equal to mgh, where m is the mass of the ball, and g is the acceleration of gravity. The kinetic energy of the ball is zero since it is not moving.

Thus, the mechanical energy of the system is equal to the potential energy of the ball at height h:

mgh = const

The height h can be expressed through the angle of inclination of the plane and the length of the rope holding the ball. To do this, you can use geometric considerations and the law of sines:

h = l*sin(60°),

where l is the length of the rope.

Then the equation for mechanical energy can be written as:

mgl*sin(60°) = const

From here we can express the pressure of the ball on the plane:

P = F/S = mg*cos(60°)/S = (12 Н)cos(60°)/(p(0.1 m)^2) ≈ 10.4 N/m^2

where F is the force with which the ball acts on the plane, S is the area of ​​contact of the ball with the plane, π is the number pi.

Thus, the pressure of the ball on a smooth inclined plane is approximately 10.4 N/m^2.

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