# Solving Spring & Elevator Homework Problem with Kinematic Equations

• NAkid
In summary, the elevator of mass 1920 kg snaps when at rest 15.6 m above a cushioning spring with a spring constant of 23100 N/m and a frictional force of 13217 N. Using the formula for work-energy, the maximum distance by which the cushioning spring will be compressed can be found by solving for the negative value of y2, which can be calculated using the work done by the friction force over the distance y1 - y2.
NAkid

## Homework Statement

The cable of an elevator of mass M = 1920 kg snaps when the elevator is at rest at one of the floors of a skyscraper. At this point the elevator is a distance d = 15.6 m above a cushioning spring whose spring constant is k = 23100 N/m. A safety device clamps the elevator against the guide rails so that a constant frictional force of f = 13217 N opposes the motion of the elevator. Find the maximum distance by which the cushioning spring will be compressed.

## Homework Equations

K1 + U(grav,1) + U(elastic,1) + W(other) = K2 + U(grav, 2) + U(elastic, 2)

## The Attempt at a Solution

I tried using the above formula for work-energy. I set my origin at the point at which the elevator initially hits the spring. So,
0 (initially at rest so K1=0) + (1920)(9.8)(15.6) + 0 (spring not yet compressed) -(13217)y2 = 0 (v2=0 so K2=0) + (1920)(9.8)y2 + .5(23100)(y2)^2

Basically I then used quadratics to solve for negative value of y2. What am I doing wrong?

NAkid said:
0 (initially at rest so K1=0) + (1920)(9.8)(15.6) + 0 (spring not yet compressed) -(13217)y2 = 0 (v2=0 so K2=0) + (1920)(9.8)y2 + .5(23100)(y2)^2
Recalculate the work done by the friction force. Over what distance does it act?

oh, should it be y1 - y2, because y2 is negative?

NAkid said:
oh, should it be y1 - y2, because y2 is negative?
Sounds right.

ok now i think my algebra is just screwy because i keep getting an incorrect answer. i have

.5k(y2)^2 + (mg - f)y2 - mgy1 + fy1 = 0

solve for negative value of y2..

Looks good to me. Just plug in the numbers and solve.

## 1. How do I approach solving a spring and elevator homework problem using kinematic equations?

The first step in solving any kinematic problem is to identify the known and unknown variables. In a spring and elevator problem, this often includes variables such as the initial and final position, velocity, and acceleration. Once you have identified the variables, you can use the appropriate kinematic equations to solve for the unknown variable.

## 2. Can I use the same kinematic equations for both the spring and the elevator in the problem?

Yes, the kinematic equations can be used for both the spring and the elevator in the problem, as long as the motion is one-dimensional. This means that the objects are only moving in one direction, either up or down. If the motion is two-dimensional, you will need to use different equations for each direction.

## 3. What is the difference between the kinematic equations for constant acceleration and variable acceleration?

The kinematic equations for constant acceleration assume that the acceleration remains constant throughout the motion. This is often the case for problems involving elevators, as the acceleration due to gravity is constant. On the other hand, variable acceleration problems involve changing acceleration, which may require the use of different equations or integration to solve.

## 4. How do I know which kinematic equation to use for a specific problem?

The kinematic equations are derived from the equations of motion, so it is important to understand the physical principles behind each equation. For example, the equation vf = vi + at is used when the initial and final velocities are known and the acceleration is constant. If the acceleration is not constant, you may need to use a different equation or integrate to solve.

## 5. Are there any common mistakes to avoid when solving spring and elevator homework problems with kinematic equations?

One common mistake is forgetting to pay attention to the direction of the motion. It is important to assign positive and negative signs to the variables based on the chosen coordinate system. Additionally, make sure to double-check your calculations and units to avoid any errors. Finally, always remember to include units in your final answer.

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