A bungee jumper of mass 60 kg jumps from a bridge tied to an elastic rope which becomes taut after he falls 10 m. Consider the jumper when he has fallen another 10 m and is travelling at 15 m/s.
Work out how much energy is stored in the rope. Take g=10 m/s^2 and ignore air resistance.
I need an answer, but I also need to know how to solve it. Thanks in advance.
60*g*20 = 12,000 J or gravitational energy will have been converted to spring and kinetic energy at that point. The kinetic part is (1/2)MV^2 = 6750 J (if you insist on using g = 10 m/s^2).
The remaining energy that must be stored in the spring is 12,000 - 6750 J.
That will give you your book answer.
Firstly you find the strain energy in the spring:
Mgh=strain energy
M: 60 kg
G: 10 m/s^2
H: 20 m
Strain energy: 60*10*20= 12000
Because you have to ignore air resistance, you just subtract the kinetic energy from the strain energy to find the energy stored in the rope
K.E = 0.5mv^2
M= 60 kg
V= 15 m/s
K.E= 0.5*60*15^2= 6750
Therefore energy in rope = 12000-6750= 5250J
energy stored: mgh=60g*20
It's from a textbook, the answer I'm supposed to get is 5250 Joules..
The h should be measure from the centre of gravity. so h is half than the total distance.
To solve this problem, we need to consider the conservation of energy. The total energy at any point in time is the sum of the kinetic energy (KE) and the elastic potential energy (PE) stored in the rope.
1. Calculate the gravitational potential energy (PEg) at the starting position:
PEg = m * g * h
where m is the mass of the jumper (60 kg), g is the acceleration due to gravity (10 m/s^2), and h is the height (initially 10 m).
PEg = 60 kg * 10 m/s^2 * 10 m = 6000 J
2. At the point where the rope becomes taut, the gravitational potential energy is converted into elastic potential energy. This happens because the rope stretches and stores energy.
PEelastic = PEg
PEelastic = 6000 J
3. When the jumper falls another 10 m and reaches a velocity of 15 m/s, calculate the kinetic energy (KE):
KE = 1/2 * m * v^2
where v is the velocity.
KE = 1/2 * 60 kg * (15 m/s)^2 = 1/2 * 60 kg * 225 m^2/s^2 = 6750 J
4. At this position, the kinetic energy is partially converted into elastic potential energy as the rope stretches further.
The total energy at this position is the sum of the kinetic energy and the remaining elastic potential energy.
Total energy = KE + PEelastic
Total energy = 6750 J + 6000 J = 12750 J
Therefore, there is 12750 J of energy stored in the rope when the jumper has fallen another 10 m and is traveling at 15 m/s.
The total energy= mgh+ 1/2mv^2
= (60*10*10)+ (60*225)/2
= 6000 + 6750
= 12750 J