Problem 17.3.16 from the collection (workbook) of Kepe O.E. 1989

17.3.16. Under the action of a pair of forces with a moment M, drum 1 of radius r = 20 cm rotates with a constant angular acceleration ε = 2 rad/s². It is necessary to determine the reaction modulus in the hinge O if the sliding friction coefficient of body 2 along the plane is f = 0.1, and the mass of load 2 is 4 kg. The mass of the drum can be neglected.

Solution: A moment of force M acts on the drum, which causes rotational acceleration ε. The sliding friction force of body 2 on the plane acts in the direction opposite to the direction of movement. The sliding friction force modulus can be calculated using the formula:

ftr = µ * N,

where µ is the sliding friction coefficient, N is the support reaction force.

The ground reaction force is equal to the sum of all forces acting on the body and is directed towards the support. In this case, the ground reaction force is directed vertically upward.

The modulus of the moment of force can be calculated using the formula:

M = I * e,

where I is the moment of inertia of the body.

Since the mass of the drum can be neglected, the moment of inertia is equal to:

I = m * r²,

where m is the mass of the load.

Then the modulus of the moment of force M is equal to:

M = m * r² * e.

Now you can find the ground reaction force. The sum of all forces acting on the body is equal to:

ΣF = N - m * g - ftr = m * a,

where g is the acceleration of gravity, a is the acceleration of the load along the plane.

The acceleration of the load along the plane is equal to the acceleration of the rotation of the drum:

a = r * e.

Then the sum of all forces acting on the body is equal to:

N - m * g - µ * N = m * r * e.

Expressing the ground reaction force, we get:

N = (m * g + µ * m * r * e) / (1 - µ).

Substituting known values, we find the reaction modulus at hinge O:

N = (4 * 9.81 + 0.1 * 4 * 0.2 * 2) / (1 - 0.1) ≈ 47.96 N.

Problem 17.3.16 in the solution book Kepe O.E. 1989

This problem is part of the collection of Kepe O.E. 1989. Solving this problem will allow us to better understand the physical laws of rotational motion of bodies.

This problem is solved using mechanics formulas, and is intended for those who have already studied the basics of physics and want to deepen their knowledge in this area.

You need to determine the modulus of reaction at the hinge O for a drum that rotates with constant angular acceleration, under the action of a couple of forces and a torque. To solve the problem, formulas are used to calculate the moment of force, the sliding friction coefficient and the support reaction force.

This task is a digital product that you can purchase in our digital goods store. After payment, the product will be available for download within a few minutes.

Product description: this task is part of the collection of Kepe O.E. 1989 and is solved using mechanics formulas. You need to determine the modulus of reaction at the hinge O for a drum that rotates with constant angular acceleration, under the action of a couple of forces and a torque. To solve the problem, formulas are used to calculate the moment of force, the sliding friction coefficient and the support reaction force. This task is a digital product that you can purchase in our digital goods store. After payment, the product will be available for download within a few minutes. The solution to the problem is done by hand, in clear, legible handwriting and saved as an image in PNG format, which will open on any device. In addition, by leaving positive feedback after purchase, you will receive a discount on your next task.

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Product description:

Solution of Kepe problem No. 17.3.16 from the collection "Dynamics" using the kinetostatic method for a rigid body and a mechanical system. The task is to determine the reaction modulus in the hinge O during rotation of drum 1 of radius r = 20 cm under the action of a pair of forces with a moment M and constant angular acceleration ε = 2 rad/s². The sliding friction coefficient of body 2 along the plane is f = 0.1, and the mass of load 2 is 4 kg. The solution to the problem is done by hand, in clear and legible handwriting, and saved as an image in PNG format, which will open on any PC or phone. After payment, you will instantly receive a solution to the problem and will be able to leave positive feedback, after which you will receive a discount on the next task.

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