# Block sliding down slope against spring

• TG3
In summary, a 4 kg block slides down a frictionless inclined plane and compresses a spring by 1.4 m before stopping. The angle of the inclined plane is 35° and the question asks for the value of the spring constant. Using the equations F=-kx and F=ma, the correct force exerted on the spring is mgsin(35) and the final value for the spring constant is -16.07.
TG3

## Homework Statement

A block with a mass of 4 kg slides from rest a distance of 2 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance 1.4 m before stopping. The inclined plane makes an angle q = 35° with the horizontal. What is the value of the spring constant?

F=-kx
F=MA

## The Attempt at a Solution

First, the force on the block = Mass (4) times acceleration. (9.81)
The force of the block when it touches the spring is 39.24.
So, the force the spring exerts is equal and opposite.
39.24 = -kx
X=1.4, so it should be easy:
39.24 = -k 1.4
-k = 28.028
k = -28.028
But this is not right...

It appears that you have everything correct except for one part. The part you have wrong is your force. You are saying the force the block exerts on the spring is mg. That is not correct. Since the block is on a ramp, only a portion of mg is put onto the spring. This portion is mgsin(35). You then set this equal to -kx or kx and solve for k.

So, to clarify, you're saying:
sine 35 x 9.81 x 4 = 22.507
22.507 = -k 1.4
16.07 = -k
-16.07 = k?
Because that answer is still being rejected... (both where k is positive and where it's negative.)

## 1. What is the purpose of studying block sliding down slope against spring?

The purpose of studying this phenomenon is to understand the principles of energy conservation and the behavior of objects when subjected to external forces such as gravity and spring force. It also has practical applications in engineering and physics, such as designing efficient braking systems or predicting the motion of objects on inclined planes.

## 2. How does the mass of the block affect its motion down the slope?

The mass of the block affects its motion down the slope as it determines the amount of force needed to overcome gravity and the spring force. A heavier block will require more force to accelerate down the slope and compress the spring, while a lighter block will require less force.

## 3. What is the role of the spring in this scenario?

The spring in this scenario acts as a source of potential energy, which is converted into kinetic energy as the block slides down the slope and compresses the spring. This helps to slow down the block's motion and eventually bring it to a stop.

## 4. How is the speed of the block affected by the stiffness of the spring?

The stiffness of the spring affects the speed of the block as it determines the amount of force needed to compress the spring. A stiffer spring will require more force to compress, resulting in a slower speed for the block. On the other hand, a less stiff spring will require less force and result in a faster speed for the block.

## 5. Can this scenario be applied to real-life situations?

Yes, this scenario can be applied to real-life situations. For example, the behavior of a car going down a hill and braking can be modeled using the principles of a block sliding down a slope against a spring. This can help engineers design safer and more efficient braking systems for cars.

• Introductory Physics Homework Help
Replies
29
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
1K
• Introductory Physics Homework Help
Replies
24
Views
1K
• Introductory Physics Homework Help
Replies
27
Views
6K
• Introductory Physics Homework Help
Replies
3
Views
491
• Introductory Physics Homework Help
Replies
3
Views
891
• Introductory Physics Homework Help
Replies
3
Views
403
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
4K
• Introductory Physics Homework Help
Replies
15
Views
1K