Newtonian - Force, Gravity, and Bungee Jumping

In summary, the problem involves a person weighing 55kg jumping off a bridge with a bungee cord attached. The goal is to find the bungee cord's force vector when the acceleration is 7.8m/s2 in the downward direction. Using the equation \SigmaF = ma, the force is calculated to be -418N. The person's weight is subtracted from the force to get the force required by the bungee cord, which is +121N.
  • #1
staycrunchy
2
0

Homework Statement


A person weighing 55kg jumps off of a bridge with a bungee cord attached. The problem seeks to find the bungee cords Force vector when the acceleration is 7.8m/s2 in the downward direction.

m = 55kg
a1 = g = 9.8m/s2

To find:
F1 when a2 = 7.8m/s2 downward.

I've specified my grid as [tex]\uparrow[/tex]+ [tex]\rightarrow[/tex]+ so the accelerations are technically negative.

Homework Equations


[tex]\Sigma[/tex]F = ma


The Attempt at a Solution


[tex]\Sigma[/tex]F = ma
[tex]\Sigma[/tex]F=55kg(-7.8m/s2)
[tex]\Sigma[/tex]F = -418N

[tex]\Sigma[/tex]F = F1 - F2
[tex]\Sigma[/tex]F = 539N - 418N
Force of bungee cord acting = +121N
 
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  • #2
Why did you subtract the forces?
 
  • #3
semc said:
Why did you subtract the forces?

The 539N was the Force with F=ma and a = g. I think I forgot to write that.
The -428N was the Force with F=ma and a = 7.8m/s2.

My inclination was to subtract the forces to get the force required by the bungee cord to slow the decent to the 7.8m/s2
 
  • #4
Well since gravitational force is downwards and he is traveling downwards...
 

FAQ: Newtonian - Force, Gravity, and Bungee Jumping

1. What is Newton's First Law of Motion?

Newton's First Law, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force.

2. How does gravity affect bungee jumping?

Gravity is the force that pulls objects towards each other. In bungee jumping, the jumper is pulled towards the Earth by the force of gravity. As the jumper falls, the bungee cord stretches and the force of gravity is counteracted, allowing the jumper to bounce back up.

3. What is the formula for calculating force?

The formula for calculating force is F=ma, where F is force, m is mass, and a is acceleration. This formula is known as Newton's Second Law of Motion.

4. How does mass affect the force of gravity?

According to Newton's Law of Universal Gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the greater the mass of an object, the greater its gravitational pull will be.

5. Can you explain the concept of terminal velocity in relation to bungee jumping?

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, such as air. In bungee jumping, the jumper's terminal velocity is reached when the force of air resistance becomes equal to the force of gravity, resulting in a constant downward speed. This is important for bungee jumping as it ensures that the jumper does not accelerate indefinitely and can be safely caught by the bungee cord.

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