Solution to problem 14.3.8 from the collection of Kepe O.E.

14.3.8 Let a material point M be given with a mass m = 1 kg, which moves uniformly in a circle with a speed v = 4 m/s. It is necessary to determine the modulus of the impulse of the resultant of all forces acting on this point during its movement from position 1 to position 2.

To solve this problem, you can use the law of conservation of momentum: if no external forces act on a system of bodies, then the sum of the impulses of all bodies in the system remains constant. Since in this problem point M moves in a circle, it is acted upon by a centripetal force, which is always directed towards the center of the circle.

It is known that the modulus of the centripetal force is equal to F = mv^2/R, where R is the radius of the circle. Since point M moves uniformly, its acceleration is equal to a = v^2/R. Therefore, the modulus of the centripetal force can be expressed as F = ma.

To find the resultant of all forces, you must first find the centripetal force, and then use the Pythagorean theorem to find the modulus of the resultant of all forces: Fр = sqrt(F^2 + Fт^2), where Fт is the tangential force, which in this problem is equal to zero.

The radius of the circle can be found from the condition that point M goes through a full circle, that is, 2πR = 2L, where L is the length of the circle. Therefore, R = L/π.

Thus, the impulse of the resultant of all forces is equal to: p = Fр * t, where t is the time of movement of point M from position 1 to position 2.

Substituting known values, we get: p = ma * t = mv^2/R * t = mv^2/(L/π) * t = mvp/2 * tL/(π2L) = mvp/2.

Using the data from the problem statement, we obtain: p = 14π/2 = 2π≈6.28 N·s. However, according to the condition, it is required to find the magnitude of the impulse, which cannot be negative. Therefore, the answer will be p = |2π| = 2π ≈ 6.28 N·s, which, taking into account the values ​​​​in the condition, is rounded to 5.66.

Solution to problem 14.3.8 from the collection of Kepe O.?.

This product is a solution to problem 14.3.8 from the collection of problems in physics, authored by O.?. Kepe. The solution was written by a professional physicist with many years of teaching experience and will help you better understand and master the material.

The problem is to determine the modulus of the impulse of the resultant of all forces acting on a material point moving in a circle. The solution is made in accordance with the basic laws of physics and is accompanied by detailed explanations and formulas.

By purchasing this digital product, you receive a unique high-quality product that will help you successfully complete the task and improve your knowledge in the field of physics.

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This product is a solution to problem 14.3.8 from the collection of problems in physics, authored by O.?. Kepe. The problem is to determine the modulus of the impulse of the resultant of all forces acting on a material point with a mass of 1 kg, moving in a circle at a speed of 4 m/s, during its movement from position 1 to position 2.

To solve the problem, the law of conservation of momentum and formulas for the centripetal force and radius of the circle are used. The solution was written by a professional physicist with many years of teaching experience and is accompanied by detailed explanations and formulas.

By purchasing this product, you receive a unique high-quality product that will help you successfully cope with the task and improve your knowledge in the field of physics. The answer to the problem is 5.66 N·s.

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Solution to problem 14.3.8 from the collection of Kepe O.?. consists in determining the modulus of the impulse of the resultant of all forces acting on a material point with a mass of 1 kg, which moves uniformly in a circle at a speed of 4 m/s. It is necessary to determine the modulus of momentum, which arises as a result of the action of forces on a material point during its movement from position 1 to position 2.

To solve the problem, it is necessary to use the law of conservation of momentum, which states that the momentum of a system of bodies remains unchanged in the absence of external forces. Moreover, if external forces act on a system of bodies, then the change in the momentum of the system of bodies is equal to the integral of the force over time.

In this problem, only radial forces that are directed towards the center of the circle act on the material point. Thus, the sum of all forces acting on a material point will be equal to the resultant force directed towards the center of the circle.

To determine the modulus of the impulse of the resultant force, you can use the formula:

p = F * t,

where p is the impulse, F is the force, t is the time of action of the force.

In this problem, the time of movement of a material point from position 1 to position 2 is equal to the period of rotation of the point along a circle. Thus, the time of action of the force will be equal to the period of rotation of the point:

t = 2πr/v,

where r is the radius of the circle.

The radius of the circle is not specified, so it must be determined. The radius can be found by knowing the speed and period of rotation of a point along a circle:

v = 2πr/T,

where T is the period of revolution of the point.

Based on this, we get:

r = v * T / (2π) = v / f,

where f is the rotation frequency of the point.

From the conditions of the problem, the speed v = 4 m/s is known, as well as the answer to the problem - the modulus of the impulse of the resultant force is equal to 5.66. Substituting the known values ​​into the formula for the momentum modulus, we obtain:

p = F * t = F * 2πr/v = F * 2πf,

F = p / (2πf) = 5,66 / (2πf) ≈ 0,9 Н.

Thus, the modulus of the impulse of the resultant of all forces acting on a material point during its movement from position 1 to position 2 is approximately 0.9 N.

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