Solution to problem 14.2.4 from the collection of Kepe O.E.

14.2.4 The force F = 3t2i + 4tj acts on the material point M. It is necessary to determine the projection of the impulse of this force onto the Ox axis over a period of time? = t2 - t1, where t2 = 2 s, t1 = 0.

Answer:

The impulse of a force is defined as the integral of this force over time:

p = ∫F dt

In this case:

p_x = ∫_t1^t2 F_x dt

where F_x - projection of force onto the Ox axis.

Substitute the expression for F:

p_x = ∫_t1^t2 3t² dt = [t³] _t1^t2 = 8 Units of measurement - N*s.

Answer: 8.

Solution to problem 14.2.4 from the collection of Kepe O..

This digital product is a solution to problem 14.2.4 from the collection of problems in physics, authored by Kepe O..

The problem is formulated as follows: a force F = 3t acts on a material point²i + 4tj. It is necessary to determine the projection of the impulse of this force onto the Ox axis over a period of time? = t₂ - t₁, where t₂ = 2 s, t₁ = 0.

This digital product provides a detailed solution to the problem using appropriate formulas and mathematical operations. The solution is presented in the form of an HTML page with a beautiful design, which makes it easier to perceive information and makes the process of studying the problem more fun and interesting.

By purchasing this digital product, you get the opportunity to improve your knowledge in the field of physics and learn how to solve problems of this type.

This digital product is a solution to problem 14.2.4 from the collection of physics problems, authored by Kepe O.?.

The problem is formulated as follows: the material point M is acted upon by a force F = 3t2i + 4tj. It is necessary to determine the projection of the impulse of this force onto the Ox axis over a period of time? = t2 - t1, where t2 = 2 s, t1 = 0.

This digital product provides a detailed solution to the problem using appropriate formulas and mathematical operations. The solution is presented in the form of an HTML page with a beautiful design, which makes it easier to perceive information and makes the process of studying the problem more fun and interesting.

By purchasing this digital product, you get the opportunity to improve your knowledge in the field of physics and learn how to solve problems of this type. The answer to the problem is 8, you will receive it as part of the solution.

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Problem 14.2.4 from the collection of Kepe O.?. consists in determining the projection of the force impulse onto the Ox axis for a given period of time.

From the conditions of the problem, the force acting on the material point M is known: F = 3t^2i + 4tj, where i and j are the unit vectors of the coordinate axes, and t is time.

It is necessary to determine the projection of the force impulse onto the Ox axis over the period of time ? = t^2 - 0, where t2 = 2 s, t1 = 0.

To solve the problem, it is necessary to calculate the force impulse for a specified period of time, and then the projection of this impulse onto the Ox axis.

The force impulse is defined as the integral of the force over time: p = ∫F dt. Substituting the expression for the force, we get:

p = ∫(3t^2i + 4tj) dt = (t^3)i + (2t^2)j

We calculate the difference in impulses at the final and initial moments of time:

Δp = p2 - p1 = (2^3)i + (2^2)j - (0)i - (0)j = 8i + 4j

Finally, the projection of the impulse onto the Ox axis is defined as the scalar product of the impulse and the unit vector of the Ox axis:

p_x = Δp · i = (8i + 4j) · i = 8.

Thus, the answer to problem 14.2.4 from the collection of Kepe O.?. equals 8.

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