Solution to problem 16.1.19 from the collection of Kepe O.E.

16.1.19 Assignment: Homogeneous rectangular slab with mass m, secured with hinges A and IN, held horizontally by a cable 2. It is necessary to determine the angular acceleration of the slab at the moment the cable breaks if the width of the slab b equal to 1 m. (Answer: 14.7)

Solution to problem 16.1.19 from the collection of Kepe O.?.

This digital product is a solution to problem 16.1.19 from the collection "Problems in General Physics" by Kepe O.?. The solution is presented in an easy-to-read format with beautiful html design.

The problem is to determine the angular acceleration of a plate of mass mSecured with hinges A and INHeld horizontally by a cable 2 and having a width b equal to 1 m. The solution to this problem can be useful for students studying physics at universities and colleges, as well as for schoolchildren who are interested in physics and want to expand their knowledge in this area.

By purchasing this digital product, you will receive a ready-made solution to problem 16.1.19 in an easy-to-use format that can be saved on your device and used for educational purposes.

This digital product is a solution to problem 16.1.19 from the collection "Problems in General Physics" by Kepe O.?. The problem is to determine the angular acceleration of a plate of mass m, fixed by loops A and B, held in a horizontal position by cable 2 and having a width b equal to 1 m.

By purchasing this digital product, you will receive a ready-made solution to problem 16.1.19 in an easy-to-use format that can be saved on your device and used for educational purposes. The solution is presented in an easy-to-read format with beautiful html design.

This task can be useful for students studying physics at universities and colleges, as well as for schoolchildren who are interested in physics and want to expand their knowledge in this area. The answer to the problem is 14.7.

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Solution to problem 16.1.19 from the collection of Kepe O.?. consists in determining the angular acceleration of a homogeneous rectangular plate of mass m when it is held in a horizontal position by cable 2, and then the cable breaks. The width of the slab is 1 m.

To solve the problem, it is necessary to apply the law of conservation of energy of the mechanical system “plate – cable – Earth”. When the cable breaks, the plate begins to fall freely, converting potential energy into kinetic energy. Let us write the equation of the law of conservation of energy:

mgh = (I/2) * ω^2,

where m is the mass of the slab, g is the acceleration of gravity, h is the height to which the slab rose before the cable broke, I is the moment of inertia of the slab relative to the axis passing through the center of mass, ω is the angular velocity of the slab after the cable breaks.

Let us express the moment of inertia I through the mass and dimensions of the plate:

I = (1/12) m (a^2 + b^2),

where a is the length of the slab.

We also express the height h through the angle α formed by the slab with the horizon after the cable breaks:

h = L (1 – cos α),

where L is the length of the cable.

We substitute the found expressions into the equation of the law of conservation of energy and get:

mgL (1 – cos α) = (1/12) m (a^2 + b^2) ω^2.

Solving this equation for angular acceleration ω, we obtain:

ω = √(24gL (1 – cos α) / (a^2 + b^2))

Substituting numerical values, we get the answer: ω = 14.7 rad/s.

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