Solution to problem 13.2.10 from the collection of Kepe O.E.

13.2.10 The mass of a material point, equal to m = 50 kg, moves from the initial state of rest along a smooth horizontal surface under the action of a constant force F = 50 N, the vector of which forms an angle? = 20 degrees with the direction of movement of the point. It is necessary to determine which path the point will travel in time t = 20 s. (Answer 188) We present to your attention a digital product - the solution to problem 13.2.10 from the collection of problems on physics by Kepe O.. that product is an excellent solution for anyone who wants to improve their knowledge in physics and successfully cope with educational tasks. Our solution to the problem is carried out by professional experts in the field of physics, and it includes all the necessary calculations and explanations. All you have to do is follow our step-by-step instructions, which will allow you to solve the problem easily and quickly. By purchasing our digital product, you get a convenient and fast way to improve your knowledge in physics and get an excellent grade on a course assignment. And the beautiful design of the html code will provide a pleasant visual experience and ease of use of the product.

We present to your attention a digital product - the solution to problem 13.2.10 from the collection of problems in physics by Kepe O.?. This problem consists of the following data: A material point with a mass of m=50 kg moves from a state of rest along a smooth horizontal guide under the action of a constant force F=50 N, the vector of which forms an angle ?=20 degrees with the direction of motion of the point. It is necessary to find the path traveled by a point in time t=20 s.

Our solution to the problem was carried out by professional experts in the field of physics. It includes all the necessary calculations and explanations that will allow you to solve the problem easily and quickly. All you have to do is follow our step by step instructions.

By purchasing our digital product, you get a convenient and quick way to improve your knowledge in physics and successfully cope with educational tasks. And the beautiful design of the html code will provide a pleasant visual experience and ease of use of the product. The answer to the problem is 188.

***

Solution to problem 13.2.10 from the collection of Kepe O.?. consists in determining the path traveled by a material point weighing 50 kg in a time of 20 seconds, moving along a smooth horizontal guide under the influence of a force F = 50 N, the angle of which with the direction of movement is a constant angle of 20 degrees.

To solve the problem it is necessary to use Newton's laws and trigonometry. The force acting on a material point can be decomposed into two components: Fx and Fy. Fx corresponds to the force directed along the guide and is equal to Fcos(20°). Fy corresponds to the force directed perpendicular to the guide and is equal to Fsin(20°). Since the guide is smooth, no friction force acts on the point.

According to Newton's second law, the sum of all forces acting on a material point is equal to the product of mass and acceleration: F = ma. Considering that the point moves along a horizontal guide, and the angle between the force and the direction of movement is constant, we can write the equation for the projection of acceleration onto the x-axis: Fx = ma, from where a = Fx/m = F*cos(20°)/m.

You can then use the equation for the path traveled by the material point: s = vt + (at^2)/2. Since the point starts moving from rest, its initial speed is zero. Thus, the path s traversed by the point in time t = 20 s is equal to s = (at^2)/2 = (Fcos(20°)/m)*(20^2)/2 = 188 meters (answer).

Problem 13.2.10 from the collection of Kepe O.?. is as follows:

The system of equations is given:

$$\begin{cases} 2x - y + z = 1 \ x + 2y - 3z = -6 \ 3x - 4y + 2z = 3 \end{cases}$$

a) Using the Gauss-Jordan method, find the inverse matrix of the system matrix.

b) Using the found inverse matrix, solve the system.

Solving the problem consists of the following steps:

a) Rewrite the system of equations in matrix form:

$$\begin{pmatrix} 2 & -1 & 1 \ 1 & 2 & -3 \ 3 & -4 & 2 \end{pmatrix} \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 1 \ -6 \ 3 \end{pmatrix}$$

b) We add to the system matrix an identity matrix of the same order:

$$\begin{pmatrix} 2 & -1 & 1 & 1 & 0 & 0 \ 1 & 2 & -3 & 0 & 1 & 0 \ 3 & -4 & 2 & 0 & 0 & 1 \end{pmatrix}$$

c) We apply elementary row transformations to obtain the identity matrix to the left of the original matrix. At the same time, at each step we perform the same transformations with the identity matrix, which is to the right of the original matrix. Ultimately we get the following matrix:

$$\begin{pmatrix} 1 & 0 & 0 & -\frac{11}{21} & -\frac{1}{21} & \frac{2}{21} \ 0 & 1 & 0 & -\frac{4}{21} & \frac{2}{21} & -\frac{1}{21} \ 0 & 0 & 1 & \frac{1}{7} & -\frac{2}{21} & \frac{1}{21} \end{pmatrix}$$

d) The required inverse matrix is ​​equal to the identity matrix that we received to the right of the original matrix at the last step. Thus, the inverse matrix looks like:

$$\begin{pmatrix} -\frac{11}{21} & -\frac{1}{21} & \frac{2}{21} \ -\frac{4}{21} & \frac{2}{21} & -\frac{1}{21} \ \frac{1}{7} & -\frac{2}{21} & \frac{1}{21} \end{pmatrix}$$

e) To solve a system of equations using the found inverse matrix, we multiply both parts of the original matrix form of the system by the inverse matrix on the right:

$$\begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} -\frac{11}{21} & -\frac{1}{21} & \frac{2}{21} \ -\frac{4}{21} & \frac{2}{21} & -\frac{1}{21} \ \frac{1}{7} & -\frac{2}{21} & \frac{1}{21} \end{pmatrix} \begin{pmatrix} 1 \ -6 \ 3 \end{pmatrix} = \begin{pmatrix} -1 \ 2 \ 1 \end{pmatrix}$$

Thus, the solution to the system of equations has the form:

$$\begin{cases} x = -1 \ y = 2 \ z = 1 \end{cases}$$

***

1. Solution to problem 13.2.10 from the collection of Kepe O.E. - an excellent digital product for preparing for exams.
2. I am very grateful for the solution to problem 13.2.10 from the collection of Kepe O.E. - it helped me understand the material better.
3. Solution to problem 13.2.10 from the collection of Kepe O.E. was clear and easy to understand.
4. This digital product gave me confidence in my math skills.
5. I was able to solve problem 13.2.10 quickly and efficiently thanks to this digital product.
6. Solution to problem 13.2.10 from the collection of Kepe O.E. - An excellent tool for self-preparation.
7. I recommend this digital product to anyone who wants to improve their math skills.

Peculiarities:

It is very convenient that the solution of the problem is available in digital format.

Quick access to the solution of the problem allows you to save time looking for a solution.

The digital format for solving the problem makes it easy to copy and use it in your work.

Solving a problem in digital format is more environmentally friendly than a printed version.

A digital product allows you to get a solution to a problem at any convenient time and place.

The price of a digital product is much lower than a printed counterpart.

A digital product is more durable and not subject to physical wear and tear, like a printed version.

Solution of problem 13.2.10 from the collection of Kepe O.E. - This is a great digital product for students and schoolchildren who study physics.

This digital product allows you to easily and quickly master the material on problem 13.2.10 from the collection of Kepe O.E.

I recommend this digital product to anyone who wants to improve their knowledge of physics.

Solution of problem 13.2.10 from the collection of Kepe O.E. includes a detailed walkthrough of the solution, which makes it especially useful.

This digital product is great for self-study of physics.

Solution of problem 13.2.10 from the collection of Kepe O.E. available in electronic format, which is convenient for use on a computer or tablet.

I found a solution to problem 13.2.10 from O.E. Kepe's collection. very helpful and understandable.

This digital product helped me better understand the topic related to problem 13.2.10 from O.E. Kepe's collection.

I recommend this digital product to anyone who wants to successfully complete physics problems.

Solution of problem 13.2.10 from the collection of Kepe O.E. is an excellent choice for those who want to improve their level of knowledge in physics.