# Sliding block with motion restricted by spring

• itsalana
In summary, we have a block of mass 2 kg attached to a spring with a relaxed length of 4 m and a spring constant of 8 N/m. The spring is initially vertical and the block is pulled 4 m to one side. The spring is extended by 1.65 m, has a potential energy stored of 10.89 J, and the block reaches a maximum speed of 3.3 m/sec when released. To find the distance the block travels when given an initial speed equal to the speed found in part (c), we can use the equation 1/2 k (x2-x1) = 1/2 k x^2, where x is the distance the block travels. Sol
itsalana
Restricted Block on Spring
A block of mass m = 2 kg slides back and forth on a frictionless horizontal track. It is attached to a spring with a relaxed length of L = 4 m and a spring constant k = 8 N/m. The spring is initially vertical, which is its the relaxed postion but then the block is pulled d = 4 m to one side.

1. By what length is the spring extended?
1.65 M OK

2. What is the potential energy stored in the spring?
10.89 J OK

3. The block is released. What is the maximum speed it attains?
3.3 m/sec OK

I need help with 4 and 5. If someone could just help me, PLEASE?!

4. Let's change the problem a bit. When the spring is vertical (hence, unstretched), the block is given an initial speed equal to 1 times the speed found in part (c). How far from the initial point does the block go along the floor before stopping?

5. What is the magnitude of the acceleration of the block at this point (when the spring is stretched farthest)?

## The Attempt at a Solution

4. So I thought that since on relaxed position, then the only work is on spring
so 1/2 k x^2 with x as 4.
When I got that number, I set that equal to 1/2k (x2-x1).
so I got a -2.72 then I subtracted that to L so 4-2.72. Then i used pythagorean and find d.
It's wrong.

I guess 3.99 and I got it right, but I have no idea how I got 3.99. It was literally a number i just typed in.

5. So for 5, with 3.99 and having no idea how I got 3.99 I don't even know where to start.

Please, if anyone could help me!
I have been working on this question for a total of 4 hours.

Last edited by a moderator:
If the block is given an initial speed at equilibrium, will it ever have a speed greater than the initial speed?

## What is a sliding block with motion restricted by spring?

A sliding block with motion restricted by spring is a simple physical system consisting of a block that can move horizontally on a frictionless surface, with its motion limited by a spring attached to a fixed point.

## How does a sliding block with motion restricted by spring work?

When the block is displaced from its equilibrium position, the spring exerts a force on it that is proportional to the displacement. This force acts in the opposite direction of the displacement, causing the block to experience simple harmonic motion.

## What factors affect the motion of a sliding block with motion restricted by spring?

The motion of the block is affected by the mass of the block, the stiffness of the spring, and the amplitude of the displacement. These factors determine the frequency and period of the motion.

## What is the equation of motion for a sliding block with motion restricted by spring?

The equation of motion for this system is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the block from its equilibrium position.

## What are the real-world applications of a sliding block with motion restricted by spring?

This system can be used in various engineering applications, such as shock absorbers, suspension systems, and vibration dampers. It is also commonly used in physics demonstrations to illustrate simple harmonic motion.

• Introductory Physics Homework Help
Replies
29
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
291
• Introductory Physics Homework Help
Replies
24
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
27
Views
6K
• Introductory Physics Homework Help
Replies
17
Views
555
• Introductory Physics Homework Help
Replies
33
Views
420
• Introductory Physics Homework Help
Replies
10
Views
364
• Introductory Physics Homework Help
Replies
3
Views
624
• Introductory Physics Homework Help
Replies
30
Views
974