Effect of Body Mass and Cord Length on Bungee Jump Motion

This essay investigates a body’s motion during a bungee jump in order to answer the question: “To what extent a body’s mass and length of the cord affect the Bungee jumping motion?” the investigation takes place with comparing three different bungee cords ‘s performance in two simulation laboratory experiments. The first is to check the relation between the bungee jumping cord and its relation to Hooke’s law and finding its elastic limit. The second is to inspect the motion in terms of velocity and acceleration changes with varying the weight of the body attached to the cord and changing the length of the cord, since they are the factors to be considered in the research question.

Introduction

Scope of work

The vine jumpers of Pentecost Island in Vanuatu inspired the spot of Bungee jumping, as it was viewed by way of a rite of passage to manhood. It is about jumping from a high point such as a bridge, a building or a crane attached to nylon braided, rubber shock cord. It is from a fixed structure most of the time but it is possible to do it from an object floating in the air, for example, a moving crane or a hot air balloon. It became a popular sport the last two decades in the United States of America where people do it for the sake of the excitement and adrenaline pumping sensations. Of course this sport involves a lot of risk and most of the accidents occurring are from miscalculations in the length of the elastic cord, which leads to many horrifying accident when people end up landing on the surface or the cord collapses, it occurred to my mind that exploring such a occurrence might be very interesting.

In this essay I aim to look at the physics behind Bungee Jumping. The aim of this essay is to investigate the factors affecting the bungee jump motion. I will be exploring the stages that the bungee jump goes through and the factors affecting it allowing a safe landing but exciting at the same time. This involves data logging from laboratory experiments and graphing data with analysis. Exploring this matter can easily make connections between fundamental concepts of physics and real world phenomena: Bungee Jumping. Therefore attempting to answer, “To what extent a body’s mass and length of the cord affect the Bungee jumping motion?”

Background information

Safety of Bungee jumping

There is no doubt that a thrilling from a height usually more than forty-five meters carries its own risk and can be very dangerous, Bungee jumping is like most adrenaline pumping sports, when done wrong, can be hazardous and even lethal.

Bungee jumping mishaps can occur because of faulty equipment or regardless of safety measures, the injuries that could have been avoided are human errors when the body strapping fails due to improper attachment or flawed harness, Chris Thomas is an example of this horrible incident, he died during a charity jump in Swansea, Wales: because of his weight[1]. Another case is cord length miscalculation and the jumper ends up hitting the ground or the bungee cord just snapped, similarly to what happened to Erin Langworthy, an Australian woman who almost drowned with her feet tied together in Zambezi River at Victoria Falls[2]. In 1989, this activity was banned in France and one state in Australia after three people faced their death[3]. And many other incidents causing people to collapse on concrete and suffer from extreme cranial trauma or even die because the rope was too long, that actually happened to Matthew E. Coleman[4], who died at an Adventure World bungee jump.

However, unavoidable injuries might occur, minor injuries such as skin burn, which is triggered through gripping the cord, happen when Bungee jumpers do not act accordingly to the guidelines given. Some of them stated that they got slapped in the face by the cord.

Other mores serious injuries; such as eyesight damage or temporary retina haemorrhage[5], strokes and traumatic carotid artery dissection happened to fit and healthy youth.

But injury inflicted by the cord, such as choking to asphyxiation, appears not to happen. This can be explained by a combination of factors, including the cord’s minimal torsional stiffness. Also, the minor pendulum motion keeps the cord from contacting the jumper and tangling or strangling him,

No modern-day jump site has seen any serious entanglement, and it is noteworthy that many participants enjoy somersaulting during the free fall without any harm or disaster occurring.

Principle components in the physics of Bungee jumping

To allow the bungee jumping motion to occur the person jumps from a high surface and the cord stretches as he is moving downwards, this demonstrates the cords’ elasticity, which can be defined as the ability of a body or the cord, in this case, to oppose a force exerted on it and change shape and size and to return to its same characteristics when the strain is removed.

The law of elasticity, Hooke’s law, determined by Robert Hooke, an English scientist in 1660, which states that, for relatively small deformations of an object, the displacement or size of the extension is directly proportional to the deforming force applied.

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Under these conditions the object returns to its original shape and size upon removal of the load.

If the force exerted exceeds a certain amount, known as the elastic limit, it would create a permanent deformation to the body even when there is no force applied on the body. The elastic limit differs from a body to another because both of the resistance to stress and it depends on what the body is made of. Elastic materials expand thinner and thinner until rupturing at their breaking point.

The strength of materials is the measurement of a body’s capacity to bear strain and stress. Stress is the internal force applied by a segment of an elastic body upon the connecting part and strain is the dimension’s deformation caused by stress. Elastic materials are the materials whose stress disappears after the exerted force is removed.

In bungee jumping the cord is subjected to pull, this is identified as tension. When the cord has weight attached and it is being pushed, this is known as a compressive stress. During the jump, the external forces twist the body around an axis, it is known as the torsional stress.

Experiment 1: Hooke’s Law

This experiment is carried out to calculate the elasticity of the bungee cord and its elastic limit.

Variables

  • Independent variables:
  • Dependent variable:
  • Control variable:

The same bungee cord used for different weights

Shape of the weight used

Height of the cord from the ground

Apparatus Used

Since the Hooke’s law experiment apparatus is usually equipped with a retort stand, which is a stand that has a ruler and a pointer attached to the spring, but since I am using a bungee cord instead of the spring, I used a regular clamp and I had seven different masses labeled 0.1 kg, a digital measuring scale with 0.01 kg uncertainty, three different car bungee cords purchased at the local hardware shop, a ruler0.0005m and a flat surface to perform the experiment on.

Method

First of all, I measure the length of the car bungee cord is provided with two hooks at each of the extremities, therefore I hang the cord with one hook on the clamp, I measure the weight holder then I hang it to the bottom hook line the I add one weight cylinder, afterwards I carefully measure the length of the cord. Next I measure each weight on the scale and I measure the extension on the cord each time the weight is added. All the measurements are recorded during the experiment.

Experiment 2: Bungee Jumping Simulation

Variables

  • Independent variables

Length of the cord

Thickness of the cord

  • Dependent variable:

Time taken to complete a bungee jump

Velocity of the body

  • Control variable:

The same bungee cord used for different weights

Shape of the weight used, using the same set of weights

Height of the weights from the motion sensor, it is controlled by placing the Vernier motion sensor on a laboratory chair with the ability to move it around and adjust its height.

Apparatus Used

Vernier motion sensor connected to a computer with a data logging software[6] installed which will be crucial for more accurate timing and graphing purposes than manual timing. Also, the same Bungee cords used in the previous Hooke’s law experiment are used since characteristics are already measured and this experiment is relating to the previous one, a meter ruler can be used to insure that the apparatus is perpendicular to the motion sensor. Blu-tack and tape is also needed.

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Method

A clamp is put on a flat surface, to prevent it from falling I and the bungee cord is hung from it with the weight holder suspended at the bottom of the cord, both of the hooks attached to both ends of the cord are secured with Blu-Tack to prevent the apparatus from falling and act as the harness in this simulation. The Vernier motion sensor is put on the laboratory chair, and before starting the experiment, activate the motion sensor and oscillate the cord with the suspended weight holder to test the sensitivity of data logging and test the range of motion detection. Afterwards the weight is elevated to the beginning of the cord and it is released with minimum to no force. This step is repeated by adding weights and the weights are secured with a thin strip of tape to avoid them falling off.

Conclusion:

Bibliography

“Aussie Plunges into Raging Waters after Bungy Cord Snaps.” N.p., 9 Jan. 2012. Web.

“BERSA.” Bersa. N.p., n.d. Web. 19 Nov. 2014.

“Bungee Jumping.” Wikipedia. Wikimedia Foundation, 18 Nov. 2014. Web. 18 Nov. 2014.

“Elasticity.” The Columbia Encyclopedia. 6th ed. N.p.: Columbia UP, 2014. Print.

“Fatal Bungee Jump Was “accident”” BBC News. BBC, 25 Feb. 2005. Web. 19 Nov. 2014.

“For Thrills, Lovers and Others Leap.” The New York Times. The New York Times, 30 July 1991. Web. 19 Nov. 2014.

“Hooke’s Law.” Encyclopedia Britannica. N.p., n.d. Web. 19 Nov. 2013.

“Hooke’s Law” The Columbia Encyclopedia. 6th ed. N.p.: Columbia UP, 2012. Print.

“Injuries Resulting from Bungee-cord Jumping.” ANNALS OF EMERGENCY MEDICINE 22.6 (1993): 1060-063. Print.

“PhysicsLAB: Springs: Hooke’s Law.” PhysicsLAB: Springs: Hooke’s Law. N.p., n.d. Web. 18 Nov. 2014.

“Relatives Grieve after Fatal Bungee Accident.” Baltimore Sun. N.p., 16 May 2000. Web. 19 Nov. 2014.

“Strength of Materials.” The Columbia Encyclopedia. 6th ed. N.p.: Columbia UP, 2012. Print.

[1] “Fatal Bungee Jump was “accident” ” BBC News. BBC, 25 Feb. 2005. Web. 19 Nov. 2014.

[2] “Aussie Plunges into Raging Waters after Bungy Cord Snaps.” N.p., 9 Jan. 2012.Web

[3] “For Thrills, Lovers and Others Leap.” The New York Times. The New York Times, 30 July 1991. Web. 19 Nov. 2014.

[4] “Relatives Grieve after Fatal Bungee Accident.” Baltimore Sun. N.p., 16 May 2000. Web. 19 Nov. 2014.

[5] “Injuries Resulting from Bungee-cord Jumping.” ANNALS OF EMERGENCY MEDICINE 22.6 (1993): 1060-063. Print.

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[6] Logger Pro 3. Portland, Or.: Vernier Software, 2003. Computer software.

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20 Examples of Law of Inertia In Everyday Life

The principle of inertia is one of the fundamental principles in classical physics that are still used today to describe the motion of objects and how they are affected by the applied forces on them. Inertia comes from the Latin word, iners, meaning idle, sluggish.

In this article, we will discuss inertia, its concept and will focus on the examples of law of inertia in everyday life.

Inertia is a passive property and does not enable a body to do anything except oppose such active agents as forces and torques .

On the surface of the Earth, inertia is often masked by gravity and the effects of friction and air resistance, both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled the philosopher Aristotle to believe that objects would move only as long as force was applied to them.

Table of Contents

What is Inertia of Motion?

law of inertia

From Newton’s first law of motion , it is clear that a body has a tendency to remain at rest or in uniform motion. This property of the body is known as inertia. Thus inertia is that property of a body due to which it opposes or resists any change in its state of rest or uniform motion.

The term inertia may be referred to as “the amount of resistance of an object to a change in velocity” or “resistance to change in motion.” This includes changes in the speed of the object or the direction of motion. One aspect of this property is the tendency of things to continue to move in a straight line at a constant speed, when no forces are affecting them.

There are Two Numerical Measures of the Inertia of a Body:

1- The Body Mass:

which governs its resistance to the action of a force.

Mass is the measure of inertia of the body; i.e., greater the mass, greater will be inertia. Thus inertia of a body depends upon its mass.

That is, massive objects possessed more inertia than lighter ones. E.g., Mass of a stone is more than a mass of a rubber ball for the same size. Therefore, the inertia of the stone is more than that of a rubber ball.

The inertial mass is a measure of the tendency of an object to resist acceleration . The more mass something has, the more it resists acceleration.

There is also gravitational mass , which as far as we can tell experimentally is identical to inertial mass.

2- The Body Moment of Inertia about a Specified Axis:

The Moment of Inertia is a measure of an object’s resistance to changes to its rotation. Also it can be defined as the capacity of a cross-section to resist bending.

It measures its resistance to the action of a torque about the same axis and i t must be specified with respect to a chosen axis of rotation and It is usually quantified in m4 or kgm2.

Moment of inertia

moment of inertia

Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion.

The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr 2 . That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.

Since the moment of inertia of an ordinary object involves a continuous distribution of mass at a continually varying distance from any rotation axis, the calculation of moments of inertia generally involves calculus, the discipline of mathematics which can handle such continuous variables. Since the moment of inertia of a point mass is defined by

The moment of inertia plays the same role in angular motion as the mass in linear motion. It may be noted that moment of inertia depends not only on mass m but also on r².

The Concept of Inertia

Inertia

The concept of inertia is a fundamental concept in physics. It is bounded with other fundamental concepts as:

The concept of state: the state of the system can be mechanical (statical, kinematical, dynamical and of deformation), thermodynamic, electromagnetic, etc. The state of a system is defined by the state parameters.

The concept of interaction.

The concept of process (transformation): Depending on the nature of the system,. The process consists in the transition of a system from a state to another. Given the causality principle, the process is the effect of interaction.

Depending on the nature of the systems and the nature of the states implied there are many types of processes: mechanical (equilibrium, motion and deformation), electromagnetic, gravitational, chemical, thermodynamic etc.

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Types of Inertia with Examples

Inertia of Rest

An object stays where it is placed, and it will stay there until you or something else moves it. The property of a body to oppose any change in its state of rest is known as inertia of rest.

Examples of Inertia of Rest in Our Daily Life

Now we will show some examples of law of inertia

Examples of law of Inertia of Rest in Our Daily Life

  • If an index card is placed on top of a glass with a penny on top of it, the index card can be quickly removed while the penny falls straight into the glass, as The cardboard moves away due to the force applied by the finger but the coin remains at its position due to inertia of rest and hence falls into the glass.
  • When a bus or a train starts suddenly, the passenger standing inside it falls backward: It happens because the feet of the passenger being in contact with the floor of the bus come in motion along with the bus but the upper part of the body remains at rest due to inertia of rest. Hence the passenger falls backward.
  • When a tree is vigorously shaken, some of the leaves fall from the tree: When the branch of a tree is vigorously shaken, the branch comes in motion as the force is applied on the branch. But the leaves want to remain at rest due to inertia of rest and fall down.
  • The carpet is beaten with a stick to remove the dust particles: When carpet is beaten with stick, the carpet comes in motion but the dust particles remain at rest due to inertia of rest.
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examples of law of inertia in rest

  • A pile of a carom coins remains intact when the lowest coin in the pile is struck quickly by a striker.

Inertia of Motion

An object will continue at the same speed until a force acts on it. The property of a body to oppose any change in its state of uniform motion is known as inertia of motion.

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Examples of Law of Inertia in Everyday Life (Inertia of Motion)

the bus stops suddenly-examples of law of inertia of motion

  • When the bus stops suddenly, people fall forward. When the driver of a bus brakes suddenly, the lower part of the body comes to rest as the bus comes to rest but the upper part of the body continues to move forward due to inertia of motion. As a result, a forward force is exerted on the body and we fall in the forward direction.
  • The electric fan continues to move for a period after the electricity is turned off. The blades of the fan were in motion. Hence, they will take time to come to rest after being switched off.
  • If you are on a train and the train is moving at a constant speed, a toy tossed into the air will go straight up and then come down. This is because the toy has inertia like the train and you.
  • Luggage is usually tied with a rope on the roof of a bus. When the bus stops suddenly, the luggage kept on the roof may fall from the roof of the bus due to inertia of motion therefore, it is advised to tie any luggage kept on the roof of a bus with a rope.

Inertia of Direction

examles of law of Inertia of Direction

An object will stay moving in the same direction unless a force acts on it. The property of a body to oppose any change in its direction of motion is known as inertia of direction.

5 Examples of Inertia of Direction

1-If you jump from a car or bus that is moving, your body is still moving in the direction of the vehicle. When your feet hit the ground, the grounds act on your feet and they stop moving. You will fall because the upper part of your body didn’t stop, and you will fall in the direction you were moving.

2-The water particles sticking to the cycle tire are found to fly off tangentially whenever a driver is negotiating a curve; the passengers experience a force acting away from the center of the curve.

3-When a bus driver is negotiating a curve on the road, passengers fall towards the center of the curved road. Whenever a driver is negotiating a curve, the passengers experience a force acting away from the center of the curve; it happens due to the tendency of the passengers to continue moving in a straight line.

4-When you stir coffee or tea and stop, the swirling motion continues due to inertia.

5- Satellites (that establish orbit around the earth) continue on their trajectory due to inertia.

Explanatory Video for Examples of law of inertia in Every day Life

The inertia of an object enables us to maintain patterns of functioning, maintain relationships, and get through the day without questioning everything. It has many important uses:

  • The design of safety devices for vehicles, including but not limited to seat belts, that can provide an external force to stop a body’s motion in the event of a sudden change in the physics of the immediate environment.
  • In space travel, for example, once a device escapes Earth’s gravity , it will continue on its given trajectory until it encounters another gravitational field or object.
  • Space probes can be sent great distances without any additional fuel required other than that needed to “escape” Earth, enact minor navigational changes or land on another object.

Examples of the Law of Inertia in Sports

Examples of the Law of Inertia in Sports

One of good examples of law of inertia in daily life is the body of a player quickly sprinting down the field will tend to want to retain that motion unless muscular forces can overcome this inertia.

A skater gliding on ice will continue gliding with the same speed and in the same direction, barring the action of an external force.

In gymnastics, athletes are constantly changing their body configuration. By increasing the radius from the axis of rotation, the moment of inertia increases thus slowing down the speed of rotation.

If an athlete wants to increase the speed of rotation, then they must decrease the radius by bringing the segments of the body closer to the axis of rotation thus decreasing the radius and moment of inertia.

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