Solution to problem 14.3.4 from the collection of Kepe O.E.

14.3.4 The momentum of the material point M changes according to the law mv = 5i+ 12tj. Determine the projection onto the Oy axis of the resultant forces applied to the point. (Answer 12)

The quantity of motion of the material point M is given, which varies according to the law mv = 5i + 12tj, where m is the mass of the point, v is its speed, i and j are the unit vectors of the coordinate axes x and y, respectively, t is time. It is necessary to determine the projection onto the Oy axis of the resultant forces applied to the point.

The resultant of forces is equal to the time derivative of the momentum: F = dp/dt = d(mv)/dt = m(dv/dt) + v(dm/dt)

Since the mass of the point is constant, then dm/dt = 0, therefore, F = m(dv/dt).

The projection of the vector F onto the Oy axis is equal to Fy = Fsin(α), where α is the angle between the vector F and the Oy axis.

Since the point moves only along the x coordinate axis, then dv/dt = 0 along the y axis. Consequently, Fy = 0, and the projection of the resultant forces onto the Oy axis is equal to 0.

Answer: 0.

Solution to problem 14.3.4 from the collection of Kepe O.?.

Our digital product is a complete solution to problem 14.3.4 from the collection of problems by Kepe O.?. in physics. In this problem, it is necessary to determine the projection onto the Oy axis of the resultant forces applied to the material point M, moving according to the law mv = 5i + 12tj, where i and j are the unit vectors of the coordinate axes x and y, respectively, m is the mass of the point, v is its speed , t - time.

Our product is an exact solution to the problem with a step-by-step description of all the necessary actions and formulas used to solve it. We also provide graphic illustrations and detailed explanations of each solution step. All this allows you not only to quickly and accurately solve this problem, but also to better understand the laws and formulas used in physics.

By purchasing our digital product, you get access to a complete solution to the problem in a format convenient for you. Our product can be useful for both students and physics teachers.

Buy our digital product and make solving physics problems easier!

Our digital product is a complete solution to problem 14.3.4 from the collection of problems in physics by Kepe O.?. In this problem, it is necessary to determine the projection onto the Oy axis of the resultant forces applied to the material point M, moving according to the law mv=5i+12tj, where i and j are the unit vectors of the coordinate axes x and y, respectively, m is the mass of the point, v is its speed , t - time.

Our product is an exact solution to the problem with a step-by-step description of all the necessary actions and formulas used to solve it. We also provide graphic illustrations and detailed explanations of each solution step. All this allows you not only to quickly and accurately solve this problem, but also to better understand the laws and formulas used in physics.

By purchasing our digital product, you get access to a complete solution to the problem in a format convenient for you. Our product can be useful for both students and physics teachers. Buy our digital product and make solving physics problems easier! Answer: the projection of the resultant forces on the Oy axis is equal to 0.

Our digital product is a detailed solution to problem 14.3.4 from the collection of problems in physics by Kepe O.?. In this problem, it is required to find the projection onto the Oy axis of the resultant forces acting on the material point M, which moves according to the law mv = 5i + 12tj, where i and j are the unit vectors of the coordinate axes x and y, respectively, m is the mass of the point, v is its speed, t - time.

To solve the problem, we use the formula F = dp/dt = d(mv)/dt = m(dv/dt) + v(dm/dt), where F is the resultant force, p is the momentum, t is time, m is the mass of the point, v is its speed.

Since the point moves only along the x-axis, then dv/dt = 0 along the y-axis. Consequently, the projection of the resultant forces on the Oy axis is equal to 0.

Answer: 0.

Our product is an exact solution to the problem with a step-by-step description of all the necessary actions and formulas used to solve it. We also provide graphic illustrations and detailed explanations of each solution step. This allows you not only to quickly and accurately solve this problem, but also to better understand the laws and formulas used in physics. Our product can be useful for both students and physics teachers. Buy our digital product and make solving physics problems easier!

***

Solution to problem 14.3.4 from the collection of Kepe O.?. consists in determining the projection onto the Oy axis of the resultant forces applied to the point M, at which the momentum changes according to the law mv = 5i + 12tj.

To solve the problem, it is necessary to determine the time derivative of the law of change of momentum in order to find the speed of movement of point M. Then, by definition, calculate the resultant of all forces acting on point M.

Next, to determine the projection onto the Oy axis, it is necessary to project the found resultant onto this axis, using the relationship between vectors and projections.

So, the projection onto the Oy axis of the resultant forces applied to point M is 12.

***

1. Solution to problem 14.3.4 from the collection of Kepe O.E. helped me prepare for my math exam perfectly!
2. A very convenient digital product - you can quickly find the task you need and check your solutions.
3. Thank you for such a detailed and understandable analysis of problem 14.3.4 from the collection of Kepe O.E.!
4. This digital product has helped me improve my math skills and improve my academic performance.
5. A very good choice for those preparing for university entrance exams.
6. Problems in the collection Kepe O.E. is a math classic, and solving Problem 14.3.4 digitally is a great way to deepen your knowledge.
7. Thanks to the authors for a high-quality and convenient digital product - I can solve problems anywhere and anytime!

Peculiarities:

An excellent solution for those who are looking for a quality digital product.

Solution of problem 14.3.4 from the collection of Kepe O.E. is a reliable assistant in teaching mathematics.

Thanks to this digital product, I was able to quickly and easily solve the problem from the collection of Kepe O.E.

A convenient format and a clear solution make this digital product an ideal choice for studying.

I recommend the solution of problem 14.3.4 from the collection of Kepe O.E. Anyone who wants to improve their knowledge in mathematics.

This digital product is a real salvation for those who are faced with difficult tasks in the collection of Kepe O.E.

Super! Solution of problem 14.3.4 from the collection of Kepe O.E. helped me get an excellent mark on the exam.