# Calculating the Force Constant of a Bungee Cord Using Newton's Laws

• evber
In summary: Notice that the acceleration in the book is wrong.In summary, the conversation discusses using a bungee cord to pull a wagon with a little sister in it. The cord's unstretched length is 1.3m and the combined weight of the sister and wagon is 295N. The person pulling the wagon accelerates from rest to a speed of 1.5m/s in 2.0s, causing the bungee cord to stretch to a length of 2.0m. The question asks for the force constant of the bungee cord, assuming it follows Hooke's law. Through calculations, the force constant is found to be approximately 30.102kg/s^2.
evber

## Homework Statement

You've attached a bungee cord to a wagon and are using it to pull your little sister while you take her for a jaunt. The bungee's unstretched length is 1.3m and you happen to know that your little sister weighs 220N and the wagon weighs 75N. Crossing a street, you accelerate from rest to your normal walking speed of 1.5m/s in 2.0s, and you notice that while you are accelerating, the bungees length increases to about 2.0 cm. what is the force constant of the bungee cord, assuming it obeys hooke's law?

f=ma
fs=kx

## The Attempt at a Solution

Ok, so I am quite stumped with this question, i know you should find the total force of the little sister and wagon , 220+75, but i do not know if i should keep it as a force or as a total mass in kg. And the difference in spring length 2.0-1.3=.7m . I am just unaware if i bring kinematic forumlas into this and i am quite unaware of what to find because i am getting the wrong answer when looking for "k"

Any guidance is appreciated. Thanks

The problem has a serious flaw, but we can ignore that for now.

I guess the 2.0 cm mean 2.0 m. The weight is a force downwards - as weight it won't help you much as your bungee cord is horizontal. Finding the mass is a good start.
What is the force needed to stretch the bungee cord? What does that force act on?

yeah its 2.0 m . long day lol . ok , so it would be total mass over gravity, giving you; 295/9.80= 30.102kg ? acceleration is 1.5/2 = 0.75 m/s^2. I don't get what you are asking in the second part though.

cant believe i had that brain fart. thanks !

Let me rephrase that: Why does the wagon accelerate, and which force (in N) comes from where?

Edit: Okay, solved?

from the pull? and i multiplied the mass and acceleration and divided by the .7m difference in the spring?

Looks fine.

## 1. What are Newton's three laws of motion?

Newton's first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

## 2. How are Newton's laws applied in everyday life?

Newton's laws are applied in everyday life in various ways, such as the motion of cars, the flight of airplanes, the bouncing of balls, and the operation of simple machines like levers and pulleys. They also explain the behavior of objects in space, including the motion of planets and satellites.

## 3. Can Newton's laws be used to solve complex problems?

Yes, Newton's laws can be used to solve complex problems in physics and engineering. These laws provide a foundation for understanding the behavior of objects in motion and can be applied to a wide range of scenarios, from simple to complex.

## 4. What is the relationship between mass and acceleration according to Newton's second law?

According to Newton's second law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that for a given force, a heavier object will have a smaller acceleration compared to a lighter object.

## 5. Are there any limitations to Newton's laws?

Yes, there are limitations to Newton's laws. These laws were developed for objects in motion under ideal conditions and do not account for factors such as air resistance, friction, and the size of objects. Additionally, these laws break down at the atomic and subatomic level, where the principles of quantum mechanics take over.

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