Solution to problem 14.3.16 from the collection of Kepe O.E.

14.3.16

Given: the body begins to move with speed v0 = 20 m/s along a rough inclined plane and stops. It is necessary to find the time of movement before stopping if the sliding friction coefficient is f = 0,1.

Answer:

According to the law of conservation of energy, the work of the friction force performed on a body when moving along an inclined plane is equal to the change in the kinetic energy of the body:

A_tr = ΔK

Where A_tr - work of friction force, ΔTO - change in kinetic energy of the body.

The work of friction force is calculated by the formula:

A_tr = F_tr * s

Where F_tr - friction force, s - the path traveled by a body when moving along an inclined plane.

The friction force is calculated by the formula:

F_tr = f * N

Where f - sliding friction coefficient, N - normal support reaction.

The normal ground reaction is calculated by the formula:

N = m * g * cos a

Where m - body mass, g - acceleration of gravity, a - the angle of inclination of the plane to the horizon.

An image of this problem can be represented as:

In this case, the body moves along an inclined plane without an initial speed in the direction of the friction force, so the acceleration of the body can be expressed as follows:

a = g * sin a - f * g * cos a

Where sin α - sine of the plane inclination angle, cos α - cosine of the plane inclination angle.

The path traveled by the body before stopping is calculated by the formula:

s = v₀ * t + (a * t²) / 2

Where t - time of movement until the body stops.

The kinetic energy of the body at the initial speed is equal to:

TO₀ = (m * v₀²) / 2

The kinetic energy of a body when stopping is equal to:

TO_con = 0

From the law of conservation of energy it follows that:

A_tr = ΔK = K0 - К_con = -(m * v₀²) / 2

Substituting expressions for friction force, acceleration and path, we get:

f * m * g * cos α * s = -(m * v₀²) / 2

Path value s can be expressed in terms of time t and acceleration a, using the following relationship:

s = v₀ * t + (a * t²) / 2

Substituting the expression for s into the equation for the friction force, we get:

f * m * g * cos α * (v₀ * t + (a * t²) / 2) = -(m * v₀²) / 2

Solving the equation for time t, we get:

t = -(m * v₀) / (2 * f * m * g * cos α - m * a)

Substituting numerical values, we get:

t = -(20) / (2 * 0.1 * 9.81 * cos 30° - 1 * (9.81 * sin 30° - 0.1 * 9.81 * cos 30°)) ≈ 3.48 с

Thus, the time of movement until the body stops is approximately 3.48 s.

Solution to problem 14.3.16 from the collection of Kepe O..

This digital product is a solution to problem 14.3.16 from the collection of Kepe O.. in physics. The solution is presented in a beautifully designed HTML document that is easy to read and use.

Problem 14.3.16 is to find the time it takes a body to move until it stops on a rough inclined plane for a given sliding friction coefficient. The solution to the problem is based on the application of the law of conservation of energy and formulas relating the force of friction, acceleration and the path traveled by the body.

This digital product can be useful to students, teachers and anyone interested in physics and problem solving. It presents a convenient and accessible way to obtain a high-quality solution to problem 14.3.16 from the collection of Kepe O..

This digital product is a solution to problem 14.3.16 from the collection of Kepe O.?. in physics. The problem is to find the time it takes a body to move before stopping on a rough inclined plane for a given sliding friction coefficient. The solution to the problem is based on the application of the law of conservation of energy and formulas relating the force of friction, acceleration and the path traveled by the body.

The digital product is presented in a beautifully designed HTML document that is easy to read and use. It can be useful to students, teachers and anyone interested in physics and problem solving. The solution is presented in a format that allows you to quickly and conveniently check the correctness of the solution and use it for your own purposes.

As a result of applying the formulas given in the solution, it was found that the time of movement until the body stops is approximately 3.48 seconds. The answer corresponds to what is specified in the task conditions.

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The product is the solution to problem 14.3.16 from the collection of Kepe O.?. The problem is to determine the time it takes a body to move along a rough inclined plane until it stops if the initial speed is 20 m/s and the sliding friction coefficient is 0.1. The answer to the problem is 3.48 seconds.

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