On a smooth horizontal surface there is a wooden

A wooden box with sand of mass M = 50 kg is located on a smooth horizontal surface. A bullet of mass m = 10 g, moving horizontally with a speed V0 = 800 m/s, hits it and gets stuck in it. It is necessary to determine the maximum deformation of the spring holding the box if its stiffness k = 1 kN/m.

To solve the problem we use the law of conservation of momentum. Since the bullet gets stuck in the box, after the collision the system (bullet + box) moves as one. Therefore, we can write:

m * V0 = (M + m) * V

Where V is the speed of the system after the collision.

From this equation we can express the speed V:

V = m * V0 / (M + m)

To determine the maximum deformation of the spring, we use Hooke's law:

F = k * x

Where F is the force acting on the spring, x is its deformation, k is the spring stiffness.

The force acting on the spring is equal to the gravitational force of the box of sand, which is located on the surface of the spring:

F = (M + m) * g

Where g is the acceleration of gravity.

Thus, the maximum deformation of the spring will be equal to:

x = F / k = (M + m) * g / k

Substituting numerical values ​​and solving the equation, we get:

x = ((50 + 0.01) * 9.81) / 1000 = 0.499 mm.

Thus, the maximum deformation of the spring holding the box is 0.499 mm.

Greetings! We are pleased to offer you a unique digital product - the e-book "Python Programming Secrets". This book will become an indispensable assistant for beginning programmers and those who are already familiar with the Python language, but want to expand their knowledge and skills.

The book contains more than 300 pages of useful information, including theoretical materials, code examples, problems and exercises. You will learn how to create programs in Python, work with databases, and use libraries for data analysis and machine learning.

The book is provided in PDF format, which allows you to comfortably read it on any device - computer, tablet or smartphone. Plus, you'll get unlimited access to online support from our team of experts who will answer any questions and help you resolve issues.

Don't miss the opportunity to purchase this unique book at a great price and take the first step towards mastering Python!

Greetings! As described in the condition of problem 10557, a wooden box with sand of mass M = 50 kg is located on a smooth horizontal surface. A bullet of mass m = 10 g, moving horizontally with a speed V0 = 800 m/s, hits it and gets stuck in it. It is necessary to find the maximum deformation of the spring holding the box if its stiffness k = 1 kN/m.

To solve the problem we can use the law of conservation of momentum. Since the bullet gets stuck in the box, after the collision the system (bullet + box) moves as one. Therefore, we can write:

m * V0 = (M + m) * V

Where V is the speed of the system after the collision.

From this equation we can express the speed V:

V = m * V0 / (M + m)

To determine the maximum deformation of a spring, we can use Hooke's law:

F = k * x

Where F is the force acting on the spring, x is its deformation, k is the spring stiffness.

The force acting on the spring is equal to the gravitational force of the box of sand, which is located on the surface of the spring:

F = (M + m) * g

Where g is the acceleration of gravity.

Thus, the maximum deformation of the spring will be equal to:

x = F / k = (M + m) * g / k

Substituting numerical values ​​and solving the equation, we get:

x = ((50 + 0.01) * 9.81) / 1000 = 0.499 mm.

Thus, the maximum deformation of the spring holding the box is 0.499 mm.

Hope this helps you solve the problem! If you have any additional questions, don't hesitate to reach out.

***

On a smooth horizontal surface there is a wooden box with sand of mass M = 50 kg. A bullet of mass m = 10 g, flying horizontally at a speed V0 = 800 m/s, hits it and gets stuck in it.

To solve the problem, it is necessary to calculate the maximum deformation of the spring holding the box if its stiffness k = 1 kN/m.

The first step is to calculate the momentum of the bullet before it hits the box. Impulse is defined as the product of a body's mass and its speed:

p = m * V0 = 10 g * 800 m/s = 8 N * s

The law of conservation of momentum states that the sum of the momentum of a system of bodies before and after a collision remains unchanged. Since the box with sand is motionless, after the collision the momentum of the system will be equal to the momentum of the bullet:

p' = p = 8 Н * с

To calculate the maximum deformation of a spring, it is necessary to calculate its potential energy, which is equal to the work done by the elastic force when the spring is deformed. The potential energy of the spring is:

Ep = (k * x^2) / 2

where k is the spring stiffness and x is the maximum deformation.

From the law of conservation of energy, we can express the maximum deformation of the spring:

Ep = p'^2 / (2 * M) = (8 N * s)^2 / (2 * 50 kg) = 6,400 J

x = sqrt((2 * Ep) / k) = sqrt((2 * 6,400 J) / 1 kN/m) = 80 mm

Thus, the maximum deformation of the spring holding the box will be 80 mm.

***

1. Great digital product! I had instant access to valuable information without having to leave my home.
2. It is very convenient to buy digital goods online, and this product is no exception. Fast delivery and easy loading process.
3. I was impressed with the quality of this digital product. The developers took a very careful approach to its creation.
4. Purchasing this digital product was easy, and using it was even easier! I'm very pleased with my purchase.
5. This digital product has been a real lifesaver for me. I had access to the information I needed anytime, anywhere.
6. An excellent choice for those who value their time and want to receive valuable information without unnecessary hassle.
7. I have had incredible fun using this digital product. It's easy to use and very useful!
8. I have used this digital product in my work and found it incredibly useful. I recommend it to all my colleagues.
9. I was pleasantly surprised when I received this digital product - it was even better than I expected! Highly recommend.
10. Thank you so much for this digital item! He helped me solve many problems and saved my time and effort.

Peculiarities:

Great additional content for an interesting game. You can get a lot of new emotions and impressions.

This DLC adds even more fun and adventure to the game. Highly recommend to anyone who has already played enough in the basic version.

Very cool and original content that will delight all House Party lovers. You won't regret your purchase!

If you were looking for something new, then this DLC is your choice. There are many unexpected scenes and endings that will make you smile.

A great way to diversify the game and add more content. Would recommend to anyone who wants to have a good time.

House Party with this DLC becomes even more interesting and exciting. New characters, places and tasks - all this will please you and make you play again and again.

It's nice that the developers continue to support the game with new content. This DLC is a great example of how you can make the game even better.