The gravitational force is almost exactly constant throughout the jump. During the bungee jumper’s fall, he or she also experiences a force due to air resistance. The faster the jumper is falling, the more the air resistance pushes back opposite to the direction of motion through the air.
What is the physics behind bungee jumping?
The bungee jump can then be divided into three phases: (i) a free-fall (with acceleration of gravity g) of the jumper, when the rope is still slack; (ii) the stretch phase until the rope reaches its maximum length; and (iii) the rebound phase consisting of a damped oscillatory motion.
How is bungee jumping calculated?
We calculate the spring constant of the bungee cord: k = F/x = mg/x = 15.2 N/m. If we release Cosmo at the position where the other end of the bungee cord is attached, he falls until the force of the stretched cord finally stops him at the bottom of his fall.
How do you calculate the extension of a bungee cord?
Equating these expressions gives mgh = 0.5kx^2. This assumes that all of the gravitational potential energy of the bungee jumper will be converted to elastic potential energy. To find the maximum extension of the rope, rearrange this expression to find x, giving x = (2mgh/k)^0.5.
What type of energy is in a bungee jump?
During a bungee jump, the stored, potential energy (PE) of the jumper on a tall platform (PE = mgh) is converted into kinetic energy (KE) during the fall (KE = 1/2mv2). This kinetic energy is converted back into potential energy as the bungee cord (rubber band chain) stretches.
What energy transfers happen in a bungee jump?
As the jumper rises, the energy in the elastic potential energy store of the rope decreases and the bungee jumper’s kinetic energy store increases until the rope becomes slack. After the rope becomes slack, and at the top of the ascent, the bungee jumper’s kinetic energy store decreases to zero.
What forces acts on a jumper?
As the jumper falls down, gravity does positive work because the force of gravity points in the same direction that the jumper falls in. The spring force of the bungee cord, however, does negative work on the jumper because the jumper is falling down while the cord is pulling up.
Why is weight important in bungee jumping?
Hooke’s Law tells us that the elastic bungee cord will stretch by a known amount for each person depending on their weight. Elastic objects stretch by the same amount each time we add the same amount of weight or force until it reaches its elastic limit.
How does elastic force work?
As you stretch or compress an elastic material like a bungee cord, it resists the change in shape. It exerts a counter force in the opposite direction. This force is called elastic force. The farther the material is stretched or compressed, the greater the elastic force becomes.
Is bungee jumping simple harmonic motion?
Bungee jumping is a good example of simple harmonic motion. Bungee jumping companies have a variety of cords so that people of different weights can take the jump without hitting the bottom. It’s similar to the egg drop lab that we did, but with different variables, and the height of the drop being the constant.
How much G force is bungee jumping?
The position y = -L is the point where acceleration a is maximum. For example, if the bungee cord weighs the same as the bungee jumper the maximum acceleration is approximately 1.6g.
What is the force constant of the bungee cord?
The bungee cord has an unstrained length of L0 = 9.00 m, and when stretched, behaves like an ideal spring with a spring constant of k = 66.0 N/m.
What is Ke formula?
Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.
Will a bungee cord forever hold its shape Why or why not?
After the elastic limit is an area called the plastic region. The object may be stretched further in this area, however it will not returned to its original shape and will be permanently distorted.
What is the spring constant formula?
Answer: When a spring is stretched, the force exerted is proportional to the increase in length from the equilibrium length, according to Hooke’s Law. The spring constant can be calculated using the following formula: k = -F/x, where k is the spring constant.
When in the bungee drop is the kinetic energy the highest?
Take the one with the positive root. The other will correspond to a height above the jumping point. The maximum kinetic energy will occur when the tension in the elastic is equal to the force of gravity on the descending jumper: so that Below this point the jumper will start to decelerate.
Does weight matter in bungee jumping?
How much you weigh will make a big difference to how the bungee jump performs, and therefore how the operators need to set it up. They will get your weight and then calculate which rope category you need to jump from. If a lighter jumper goes first, they will have a different rope to a heavier jumper who goes next.
What happens during a bungee jump?
The thrill comes from the free-falling and the rebound. When the person jumps, the cord stretches and the jumper flies upwards again as the cord recoils, and continues to oscillate up and down until all the kinetic energy is dissipated.
How is energy transferred physics?
Thermal energy transfers occur in three ways: through conduction, convection, and radiation. When thermal energy is transferred between neighboring molecules that are in contact with one another, this is called conduction.
How is energy transferred to the jumper?
As the jumper falls, energy is transferred from the gravitational potential energy store to the kinetic energy store. When the bungee rope just starts to tighten, the kinetic energy store is now at its maximum. All the energy has been transferred to elastic potential energy store.
How do you reduce unwanted energy transfers?
There are two main ways to reduce unwanted energy transfers by heating: use insulator – materials with low thermal conductivity ; use thicker materials.
Which of Newton’s Laws explains bungee jumping?
NET FORCE= F(bungee)-F(earth)=0 The forces acting on the object are equal in size, but opposite in direction. Newton’s third law can also be applied to the entire bungee jumping system. This law can be applied as the bungee jumper is falling.
How do you calculate jump height in physics?
Derive the formula vi = -g*T/2 from the formula sf = si + vi*T + (g*T²)/2. The initial and final positions are the same before and after the jump, so set them to zero and factor: T(vi + g*T/2) = 0. Setting the factors equal to zero gives you two results: T = 0 and vi + g*T/2 = 0.
How does the law of inertia apply to bungee jumping?
When a bungee jumper is falling, the property of inertia explains how they want to keep falling. The object in movement, the bungee jumper, wants to stay in motion, as we know because if there was not an external force, such as the bungee or the ground, the bungee jumper would continue to fall.
Who should not bungee jump?
Bungee jumping may have health risks for people who are overweight or with injuries. Pregnant women, people with heart problems and high blood pressure are not advised to do bungee jumping.