Let us consider a situation in which a body moves along an inclined rough plane forming an angle of 40° with the horizon. It is necessary to determine the acceleration of a body with a sliding friction coefficient of 0.3.
The solution to this problem can begin by determining the forces acting on the body. In this case, we have a gravity force directed downward in the direction of the plane's inclination, as well as a frictional force directed upward in the direction of the plane's inclination. Taking into account the sliding friction coefficient, we can write:
Ftr = f * N,
where Ftr is the friction force, N is the normal reaction of the support, f is the sliding friction coefficient.
The normal support reaction, in turn, is equal to the weight of the body projected onto an axis perpendicular to the plane:
N = m * g * cos(α),
where m is the mass of the body, g is the acceleration of gravity, α is the angle of inclination of the plane.
Now we can write down the equation of motion of a body along an inclined plane:
m * a = m * g * sin(α) - Fтр,
where a is the acceleration of the body.
Substituting expressions for Ftr and N, we get:
m * a = m * g * sin(α) - f * m * g * cos(α),
from where we express a:
a = g * (sin(α) - f * cos(α)).
Substituting the values of the plane inclination angle and the sliding friction coefficient, we obtain:
a = 9.81 м/с² * (sin(40°) - 0.3 * cos(40°)) ≈ 4.05 m/s².
This problem considers the movement of a body along an inclined rough plane at an angle of 40° to the horizontal. It is necessary to find the acceleration of the body, provided that the sliding friction coefficient is 0.3. To solve the problem, it is necessary to determine the forces acting on the body, namely: gravity and friction. After this, you can write down the equation of motion and, substituting known values, find the acceleration of the body. The answer obtained is 4.05 m/s².
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This digital product is a unique solution to problem 13.2.3 from the collection of Kepe O.?. The problem is to determine the acceleration of a body moving down an inclined rough plane at an angle of 40° to the horizontal with a sliding friction coefficient of 0.3. Solving the problem begins with determining the forces acting on the body, namely: gravity and friction. Then the equation of motion is written down and, by substituting known values, the acceleration of the body is found. The solution to the problem is presented in the form of a beautiful HTML document, which allows you to conveniently view and study the material on any device. By purchasing this product, you get access to a complete and detailed solution to the problem, which will help you better understand the theory and strengthen practical skills in solving problems in physics.
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Solution to problem 13.2.3 from the collection of Kepe O.?. consists in determining the acceleration of a body moving down an inclined rough plane, the angle of inclination of which to the horizon is 40°, provided that the sliding friction coefficient is 0.3.
To solve the problem it is necessary to use the laws of dynamics and the theory of friction. According to Newton's second law, the sum of all forces acting on a body is equal to the product of the body's mass and its acceleration: ΣF = ma.
In this problem, two forces act on the body: gravity and friction. The force of gravity is directed vertically downwards and is equal to the mass of the body multiplied by the acceleration of gravity g: Fg = mg. The friction force is directed along the surface of the inclined plane and is equal to the product of the sliding friction coefficient f and the normal force N: Ftr = fN.
The normal force N is equal to the projection of gravity onto the axis perpendicular to the surface of the plane: N = mgcosα, where α is the angle of inclination of the plane to the horizon.
Thus, the sum of all forces acting on the body along the plane is equal to: ΣF = Fpr - Ftr = mg(sinα - fcosα), where Fpr is the projection of gravity onto the axis parallel to the surface of the plane.
From Newton's second law it follows that the acceleration of a body is equal to the ratio of the sum of all forces to the mass of the body: a = ΣF/m. Substituting the expression for the sum of all forces into this formula, we get:
a = g(sinα - fcosα) = 9.81 m/s² × (sin40° - 0.3cos40°) ≈ 4.05 m/s².
Thus, the acceleration of a body moving down an inclined rough plane is approximately 4.05 m/s², provided that the sliding friction coefficient is 0.3.
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