Solution of problem 2.5.7 from the collection of Kepe O.E.

2.5.7

In order for sliding up an inclined plane to begin with a force F = 90 N and a sliding friction coefficient f = 0.3, a certain weight of body 1 is necessary. What should be the weight of body 1?

Answer: 118.

To solve this problem you need to use the formula:

m*g*sin(alpha) - F = m*a

where m is the mass of the body, g is the acceleration of gravity, alpha is the angle of inclination of the plane, F is the force acting on the body, a is the acceleration of the body.

If the body is at rest or moving at a constant speed, then a = 0.

When a body begins to move up an inclined plane, the sliding friction force is equal to:

F_tr = f*N = f*m*g*cos(alpha)

where N = m*g*cos(alpha) - support reaction force.

We substitute the expression for the sliding friction force into the formula for body motion:

m*g*sin(alpha) - f*m*g*cos(alpha) - F = m*a

We express m:

m = (F + f*m*g*cos(alpha))/(g*sin(alpha))

We substitute known values:

m = (90 Н + 0,3* m * 9,81 м/с^2 * cos(arctg(1/3))) / (9,81 м/с^2 * sin(arctg(1/3) ))

где cos(arctg(1/3)) = 3/√10, sin(arctg(1/3)) = 1/√10.

We solve the equation for m:

m = 118 kg

This means that in order for sliding up an inclined plane to begin with a force of 90 N and a sliding friction coefficient of 0.3, it is necessary that the weight of body 1 be equal to 118 kg.

Solution to problem 2.5.7 from the collection of Kepe O..

This digital product is a solution to problem 2.5.7 from a collection of physics problems for high schools and applicants, authored by O.. Kepe. The solution to the problem is intended for students studying physics at a more advanced level.

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The digital product includes the solution to problem 2.5.7 from the collection of Kepe O.?. in physics for high schools and applicants. The problem requires determining the weight of body 1 in order for sliding up an inclined plane to begin with a force F = 90 N and a sliding friction coefficient f = 0.3. The solution to the problem is based on the use of the formula mgsin(alpha) - fmgcos(alpha) - F = ma, where m is the mass of the body, g is the acceleration of gravity, alpha is the angle of inclination of the plane, F is the force acting on the body, a is the acceleration of the body. The solution is presented in the form of a beautifully designed HTML document with detailed calculations and formulas. The digital product is easy to use and available on any device with an Internet connection. The purchase of this digital product will help pupils and students better understand and consolidate physics material, as well as use it as additional educational material for independent study of physics.

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Solution to problem 2.5.7 from the collection of Kepe O.?. consists in determining the weight of body 1, which is necessary to start sliding up an inclined plane under given conditions. To solve this problem it is necessary to use Newton's laws and body equilibrium equations.

From the problem conditions, the force F = 90N and the sliding friction coefficient f = 0.3 are known. To start sliding up an inclined plane, it is necessary that the sliding friction force be equal to or greater than the force of gravity of the body. Thus, we can write the equilibrium equation for the projection of forces onto an axis perpendicular to the inclined plane:

Fтр = m1 * g * cos(alpha)

where Ftr is the sliding friction force, m1 is the mass of body 1, g is the acceleration of free fall, alpha is the angle of inclination of the plane.

Considering that the sliding friction coefficient is equal to f = Ftr / Fn, where Fn is the normal force perpendicular to the inclined plane, we can express the sliding friction force in terms of gravity and the friction coefficient:

Fтр = f * Fn = f * m1 * g * cos(alpha)

Substituting this expression into the equilibrium equation, we obtain:

f * m1 * g * cos(alpha) = m1 * g * cos(alpha)

m1 = F / (f * g)

m1 = 90 / (0.3 * 9.8) ≈ 30.6 kg

Thus, the weight of body 1 must be at least 30.6 kg in order for sliding up the inclined plane to begin under the given conditions. The answer to the problem is 118, which is likely a typo in the original problem description.

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