Stuck on spring displacement

In summary, the magnitude of the spring's displacement at the instant when the acceleration of the box is zero is given by the algebraic expression F = KX, where F is the force of the spring, K is the spring constant, and X is the displacement of the spring. Using the equation V^2 = KX^2/M, the value of X can be calculated to be approximately 0.0308 meters, but this may be incorrect if the equation is rearranged incorrectly. To solve for X, all forces acting on the box, including gravity, must be taken into account.
  • #1
Paulbird20
53
0
Suppose the spring has a spring constant of 350 N/m and the box has a mass of 1.8 kg. The speed of the box just before it makes contact with the spring in 0.43 m/s.

What is the algebraic expression for the magnitude of the spring's displacement at the instant when the acceleration of the box is zero? Express your answer in terms of the mass m of the block, the spring constant k, and the magnitude g of the acceleration due to gravity. (Answer using m to be the mass of the block, k to be the spring constant, and g to be the acceleration due to gravity).
Magnitude of spring's displacement = ?

Ok, from my notes i have spring F = K(constant for spring) * change in distance.

and also

V^2 = K* X^2 / M(mass)

and i re arranged that to V^2* M / K = X^2
i used this equation to get X = .0308 (meters?) and it shows as incorrect.

I think i may have re arranged the equation wrong but I am not sure any help would be great. TY
 
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  • #2
Paulbird20 said:
Suppose the spring has a spring constant of 350 N/m and the box has a mass of 1.8 kg. The speed of the box just before it makes contact with the spring in 0.43 m/s.

What is the algebraic expression for the magnitude of the spring's displacement at the instant when the acceleration of the box is zero? Express your answer in terms of the mass m of the block, the spring constant k, and the magnitude g of the acceleration due to gravity. (Answer using m to be the mass of the block, k to be the spring constant, and g to be the acceleration due to gravity).
Magnitude of spring's displacement = ?

Ok, from my notes i have spring F = K(constant for spring) * change in distance.

and also

V^2 = K* X^2 / M(mass)

and i re arranged that to V^2* M / K = X^2
i used this equation to get X = .0308 (meters?) and it shows as incorrect.

I think i may have re arranged the equation wrong but I am not sure any help would be great. TY
No acceleration implies Newton 1. Identify all forces acting and apply it. I assume the box is falling vertically?
 
  • #3


Hello,

Thank you for sharing your notes and equations. It seems like you are on the right track, but there may be some slight errors in your calculations. Let's break down the problem and see if we can find the correct answer.

First, let's review the given information:

- Spring constant (k) = 350 N/m
- Mass of the box (m) = 1.8 kg
- Initial velocity of the box (v) = 0.43 m/s

We also know that:

- Force (F) = mass (m) * acceleration (a)
- The acceleration of the box is zero at the instant when the spring's displacement is at its maximum.

Now, let's use the equations you provided to find the spring's displacement at the instant when the acceleration of the box is zero:

- From F = kx, we can rearrange to find x: x = F/k
- From v^2 = kx^2/m, we can rearrange to find x: x = v^2*m/k

Substituting the given values, we get:

- x = (1.8 kg * 0.43 m/s^2) / 350 N/m = 0.0022 m
- x = (0.43 m/s)^2 * 1.8 kg / 350 N/m = 0.0022 m

These calculations give us the same result, which is the displacement of the spring at the instant when the acceleration of the box is zero. Therefore, the algebraic expression for the magnitude of the spring's displacement is:

x = (m * v^2) / k

I hope this helps clarify the problem and how to find the correct answer. Keep up the good work in your studies!
 

1. What is spring displacement?

Spring displacement refers to the distance a spring moves from its original position when it is stretched or compressed. It is typically measured in meters (m) or centimeters (cm).

2. How is spring displacement calculated?

Spring displacement is calculated by subtracting the spring's original length from its final length after being stretched or compressed. The formula is: displacement = final length - original length.

3. What factors affect spring displacement?

Spring displacement is affected by the force applied to the spring, the spring's stiffness (also known as the spring constant), and the mass attached to the spring. The displacement will increase if the force or mass increases, and decrease if the spring stiffness increases.

4. How does spring displacement relate to Hooke's Law?

Spring displacement is directly proportional to the force applied to the spring, as stated in Hooke's Law. This means that if the force is doubled, the displacement will also double. However, Hooke's Law is only applicable for small displacements and only works for linear springs.

5. Why is spring displacement important in mechanical systems?

Spring displacement is important in mechanical systems because it affects the overall behavior and performance of the system. By understanding and controlling the displacement of springs, engineers can design and optimize systems to function effectively and efficiently.

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