# How Does Spring Compression Relate to Ramp Angle and Friction in Equilibrium?

• hello95
In summary, the block of mass M rests on a ramp inclined at an angle z. There is a coefficient of friction s between the block and the ramp. The ramp itself rests on a horizontal, frictionless surface and is held away from the wall by a spring with spring constant k. The compression of the spring is dependent on which force is greater: force 1 (acting parallel to the surface of the ramp) or force 2 (acting perpendicular to the surface of the ramp).
hello95

## Homework Statement

A block of mass M rests on a ramp inclined at an angle z. there is a coefficient of friction s between the block and the ramp. The ramp itself rests on a horizontal, frictionless surface and is held away from the wall by a spring with spring constant k. What is the compression of the spring if the system is in equilibrium? (Hint: This is a conceptual problem; there is a visualization that eliminates the need for an equation.)

-

## The Attempt at a Solution

The way I see it, there are two horizontal forces acting on the inclined plane:

1: The component of the force due to friction (acting at angle z from the horizontal - or along the surface of the plane) on the block parallel to the horizontal (exerted by the block). The way I visualize this is if one were to have a small inclined plane on a table, one could push it along by pressing a finger on the plane's surface at an angle to the table. (this force acts away from the spring)

2: The component of (the component of the force due to gravity exerted on the block that is perpendicular to the surface of the block (i.e: opposite to the normal force)) that is parallel to the horizontal, frictionless surface. (this force acts towards the spring)

Now, it could be that with the right angle or coefficient of static friction, the plane would not move at all according to these assumptions, however whether the spring compressed or not would depend on which force was greater - force 1 or force 2.

Am I visualizing this correctly?

I apologize if I haven't explained myself well enough, if any clarification is needed please let me know.

I think no compression at all, since the CM remains.

Sorry, what do you mean by CM?

Sorry I'm was wrong on the compression since the block moves away from the center of mass.
This follows by the ramp moving in opposite direction according to conservation of momentum and compressing the spring.
The compression must be the ratio of the 2 masses.

hello95 said:
The way I see it, there are two horizontal forces acting on the inclined plane:

1: The component of the force due to friction (acting at angle z from the horizontal - or along the surface of the plane) on the block parallel to the horizontal (exerted by the block). The way I visualize this is if one were to have a small inclined plane on a table, one could push it along by pressing a finger on the plane's surface at an angle to the table. (this force acts away from the spring)
Correct.

hello95 said:
2: The component of (the component of the force due to gravity exerted on the block that is perpendicular to the surface of the block (i.e: opposite to the normal force)) that is parallel to the horizontal, frictionless surface. (this force acts towards the spring)

If you meant the horizontal component of the normal force between body and ramp then it is correct.
hello95 said:
Now, it could be that with the right angle or coefficient of static friction, the plane would not move at all according to these assumptions, however whether the spring compressed or not would depend on which force was greater - force 1 or force 2.

Am I visualizing this correctly?

The system is in equilibrium, so both parts, block and ramp, are in equilibrium.
I think you are on the right track, but you have to consider the forces (gravity, normal force, friction) acting also on the body. You have two equations there, both for the components parallel with the slope and normal to it.
Write up all the three equations of equilibrium (one for the horizontal components of the forces acting on the ramp and the other two for the body and figure out the relations between them and see at what compression can be equilibrium maintained with the condition that the force of friction can not be greater than the normal force times coefficient of friction.

ehild

azizlwl said:
Sorry I'm was wrong on the compression since the block moves away from the center of mass.
This follows by the ramp moving in opposite direction according to conservation of momentum and compressing the spring.
The compression must be the ratio of the 2 masses.

The system is in equilibrium: neither part is moving.

ehild

## 1. What is the purpose of studying physics?

The purpose of studying physics is to understand the fundamental laws and principles governing the natural world. It helps us explain and predict the behavior of matter and energy, from the smallest particles to the largest structures in the universe.

## 2. What are some common misconceptions about physics?

One common misconception is that physics is only for geniuses or extremely intelligent individuals. In reality, anyone can understand and appreciate the concepts of physics with proper guidance and effort. Another misconception is that physics is all about complicated mathematical equations, when in fact it is about understanding the fundamental principles behind those equations.

## 3. How does physics play a role in everyday life?

Physics plays a crucial role in everyday life. It is the foundation of modern technology, including electronics, transportation, energy production, and communication. It also helps us understand natural phenomena such as weather, light, and sound, and allows us to develop solutions to real-world problems.

## 4. What are some current unsolved problems in physics?

Some current unsolved problems in physics include the unification of the four fundamental forces (gravity, electromagnetism, strong and weak nuclear forces), the nature of dark matter and dark energy, and the origin of the universe. These are complex and challenging problems that scientists are continuously working on.

## 5. How can one improve their understanding and problem-solving skills in physics?

To improve one's understanding and problem-solving skills in physics, it is important to practice regularly and consistently. This includes solving a variety of problems, reading and understanding textbooks and lectures, and seeking help from teachers or peers when needed. It is also helpful to make connections between different concepts and to constantly ask questions and seek deeper understanding.

• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
31
Views
1K
• Introductory Physics Homework Help
Replies
16
Views
889
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
36
Views
4K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
1K