# Spring Car, Acceleration Problem: Find Spring Constant

• Jaccobtw
In summary, the conversation discusses the calculations and equations needed to determine the acceleration and spring constant for a spring that can accelerate from rest to 20 m/s 50 times before needing to be rewound. It is determined that the spring must unwind 0.042 m 50 times for a total distance of 2.1m, and the acceleration is calculated to be 4,762 m/s^2. The spring constant is found to be 5.7 * 10^7 N/m. However, it is noted that the energy stored in the spring increases with the square of the displacement, so the first 0.042 m unwound releases more energy than subsequent amounts.

#### Jaccobtw

Homework Statement
You devise a wound up car powered by a spring for trips to the grocery store. The car has an inertia of 500 kg and is 4.2 m long. It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding. The spring runs the length of the car, and a full winding compresses it to half of its length In order to meet the acceleration requirement, what must the value of the spring constant be?
Relevant Equations
F = ma
F = -kd
"It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding"
-So F = -kd = -k(2.1) - d is 2.1 because it is the compression length

Now, since we know the d, divide it by 50, 2.1/50 = 0.042m

Basically, the spring unwinds 0.042 m 50 times for a total distance of 2.1m.

Now, calculate acceleration:
v(f)^2 = v(i)^2 * 2 * a * d

We know our final velocity is 20 m/s, our initial is 0.

Solving for a we get, 4,762 m/s^2

Back to our original equations

F = -kd = ma

Solve for k and we get : 5.7 * 10^7 N/m

But I got this wrong :(

Jaccobtw said:
the spring unwinds 0.042 m 50 times
No. The energy stored in a spring rises as the square of the displacement, so the first 0.042 m it unwinds releases more energy than the next 0.042 m, etc.
Instead of forces, work with energy.

Jaccobtw

## 1. What is a spring car acceleration problem?

A spring car acceleration problem involves a car being attached to a spring and released from a certain height. The goal is to determine the spring constant, which is a measure of the stiffness of the spring, based on the acceleration of the car.

## 2. How do you solve a spring car acceleration problem?

To solve a spring car acceleration problem, you need to measure the distance the car falls from before it is attached to the spring, the time it takes for the car to reach the bottom of the spring, and the mass of the car. Then, you can use the equation F = ma = kx to calculate the spring constant, where F is the force applied by the spring, m is the mass of the car, a is the acceleration, and x is the distance the spring is compressed.

## 3. What factors can affect the accuracy of the spring constant calculation?

The accuracy of the spring constant calculation can be affected by factors such as air resistance, friction between the car and the surface it is released from, and the elasticity of the spring. These factors can introduce errors in the measurements and result in a slightly different value for the spring constant.

## 4. How is the spring constant related to the stiffness of the spring?

The spring constant is directly proportional to the stiffness of the spring. This means that a higher spring constant indicates a stiffer spring, while a lower spring constant indicates a less stiff spring. The stiffness of a spring determines how much force is needed to compress or stretch it by a certain distance.

## 5. What are some real-life applications of a spring car acceleration problem?

A spring car acceleration problem can be used to study the behavior of materials and their elasticity, as well as to determine the stiffness of springs used in various devices such as shock absorbers, car suspensions, and pogo sticks. It can also be used in sports science to analyze the performance of athletes in activities such as long jump and pole vaulting.