Problem 17.3.15 from the collection (workbook) of Kepe O.E. 1989

17.3.15. It is necessary to calculate the modulus of reaction of the hinge O, if a load of mass m2 = 5 kg under the influence of gravity is lowered with an acceleration a = 3 m/s2. The mass of block 1 is m1 = 10 kg, and its center of mass is on the axis of rotation.

To solve this problem, it is necessary to use the equilibrium equation of a rotating body:

ΣM = Iα,

where ΣM is the sum of the moments of forces, I is the moment of inertia of the body, α is the angular acceleration.

In this problem, block 1 is at rest, so its angular acceleration is zero. Therefore, the sum of the moments of forces acting on the system must be equal to zero:

ΣM = 0.

The moment of gravity acting on a load of mass m2 is equal to:

M = m2gR,

where g is the acceleration due to gravity, and R is the radius of the hinge.

The moment of inertia of the system relative to the axis of rotation is equal to:

I = m1R^2,

where R is the distance from the axis of rotation to the center of mass of block 1.

Thus, the equilibrium equation of a rotating body can be written as:

m2gR - Fр = Iα,

where Fр is the reaction of the hinge, and α is the angular acceleration of the load.

Considering that the angular acceleration of the load is related to its linear acceleration by the following relationship:

α = a/R,

where a is the linear acceleration of the load, we get:

m2gR - Fр = m1R^2(a/R).

From here we express the reaction of the hinge Fр:

Fр = m2gR - m1Ra.

Substituting known values, we get:

Fр = 5 kg × 9.8 m/s^2 × R - 10 kg × 3 m/s^2 × R = (49R - 30R) Н = 19R Н.

Thus, the reaction modulus of the hinge O is 19R N.

Product description

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Product description:

It is proposed to purchase the solution to problem No. 17.3.15 from the collection of Kepe O.E. 1989. In this problem, it is required to determine the modulus of reaction of the hinge O, if load 2 with a mass of m2 = 5 kg is lowered under the influence of gravity with an acceleration of a = 3 m/s2. The mass of block 1 is equal to m1 = 10 kg, and its center of mass is located on the axis of rotation.

After payment, you will receive the solution to Kepe problem No. 17.3.15 in PNG format, handwritten in clear and legible handwriting. The solution will open on any device, including PC and phone.

After purchasing the solution, leave a positive review and receive a discount on the next task.

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