# Block on Incline with oscillation

• soccer_09
In summary, the problem involves a block on a frictionless incline connected to a spring with a given length and constant. The question asks for the block's position on the incline to prevent oscillation. By setting the force of the spring equal to the force of gravity, the correct formula to use is x = [mg cos(theta)]/k. This results in a distance of 1.284 m. Some confusion may arise from the given weight of 17.0 N, which is actually equal to the force of gravity, not mass times gravity.
soccer_09

## Homework Statement

Block on Incline In Fig. 16-35, a block weighing 17.0 N is able to slide without friction on a 32.0° incline. It is connected to the top of the incline by a massless spring of unstretched length 0.475 m and spring constant 110 N/m.

Figure 16-35

(a) How far down the incline would you have to place the block so it would not oscillate when you let go?
1 m
(b) If the block is pulled slightly down the incline from where you placed in part (a) and released, what is the period of the resulting oscillations?

## Homework Equations

I got part b, just need part a.

I was told that Force(spring) = Force(gravity)

(Fs) = kx
(Fgrav)= mgcos(theta) since on an incline

## The Attempt at a Solution

The force of spring = kx and
The force of grav = mg cos(theta)

By doing this my answer should be x = [ mg cos (theta) ] / k
which comes out to be about 1.284

This showed up as incorrect. Some guidance about what I'm doing wrong is greatly appreciated.

I had posted in another thread a few hours ago and no one responded... but it was one that already had many posts so I guess people just ignored it.

Force of gravity = mg*sin(theta)

I already tried that and it was wrong. I got .8026 for my answer and I even tried doing sin and cos of 40 degrees. None of them worked. I looked on cramster and found the same problem since no one had been answering my other post and I found that they got the right answer using the formula I stated above. Their m was 10 N, k was 150 and theta was I believe 37 or 38, I think 38 and the answer was .515 and correct. Having really bad luck I guess. Anything else you might suggest I try? I really can't think of another formula that would work.

I figured it out. They give the weight as 17.0 N which is mg so I was doing g squared at first. When I got my answer with that, I added it to the initial distance and got it right. Got it on the 10th try out of 10 as well :) Thanks for trying though hehe. Was just a pure coincidence that the cos worked for the other problem.

## 1. What is a "Block on Incline with oscillation"?

A "Block on Incline with oscillation" refers to a physical system consisting of a block placed on an inclined plane that is undergoing periodic oscillations. This setup can be used to study the effects of oscillation on the motion of the block.

## 2. How does the angle of inclination affect the behavior of the block?

The angle of inclination of the plane affects the acceleration of the block. As the angle increases, the acceleration of the block decreases due to the increase in the component of gravity acting against the motion of the block.

## 3. What is the relationship between the amplitude of oscillation and the acceleration of the block?

The amplitude of oscillation, or the maximum displacement of the block from its equilibrium position, is directly proportional to the acceleration of the block. This means that as the amplitude increases, the acceleration of the block also increases.

## 4. How does the frequency of oscillation affect the motion of the block?

The frequency of oscillation, or the number of oscillations per unit time, affects the speed of the block. As the frequency increases, the speed of the block also increases, resulting in a shorter period of oscillation.

## 5. What factors can affect the energy of the block in this system?

The energy of the block in this system can be affected by the amplitude, frequency, and angle of inclination. Friction between the block and the inclined plane can also affect the energy of the system.

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