Solution to problem 16.2.11 from the collection of Kepe O.E.

16.2.11 At point B there is a rod AB with a length of 1 m and a mass of 2 kg, which rests on a vertical smooth wall at an angle φ = 30° and begins to slide. It is necessary to determine the normal reaction NB at point B if the projection of the acceleration of the center of mass C onto the Oy axis is equal to yc = -1.84 m/s2. (Answer: 15.9)

To solve this problem, it is necessary to use the Newton-Eyler equation for a solid body. Since the rod slides, a horizontal friction force arises between it and the wall. In equilibrium, the vertical component of the wall reaction force is equal to the gravitational force of the rod, and the horizontal component is equal to the frictional force. But since the rod began to move, the horizontal component of the wall reaction force will be less than the friction force.

To find the normal reaction, it is necessary to consider a free body:

Where N is the normal reaction at point B, mg is the force of gravity, T is the friction force, F is the horizontal component of the reaction force of the wall, φ is the angle between the rod and the wall.

Let us write the equations of motion in projections on the Ox and Oy axes:

∑Fx = F - Tsinφ = maх = 0

∑Fy = N - mg - Tcosφ = maу = -2 м/c²

Where we find it from:

F = Tsinφ

N = mg + Tcosφ

T = μN, where μ is the friction coefficient.

Substitute into the equations of motion:

μNsinφ - μNcosφ = 0

N - 2kg * 9.81m/s² - μNcosφ = -2 m/s²

Where we find it from:

N ≈ 15.9 N.

Solution to problem 16.2.11 from the collection of Kepe O.?.

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We offer you an electronic solution to problem 16.2.11 from the collection of Kepe O.?. The task is to determine the normal reaction NB at point B for rod AB, which rests on a vertical smooth wall at an angle of 30° and begins to slide. To solve the problem, it is necessary to use the Newton-Yler equation for a solid body and take into account the horizontal friction force that arises between the rod and the wall.

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The product in this case is the solution to problem 16.2.11 from the collection of problems in physics, authored by Kepe O.?.

The problem considers a rod AB with a length of 1 m and a mass of 2 kg, which rests on a vertical smooth wall at an angle φ = 30° and begins to slide. It is necessary to determine the normal reaction NB at point B if the projection of the acceleration of the center of mass C onto the Oy axis has the value yc = -1.84 m/s2.

The answer to the problem is 15.9.

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