Qns type 1
A metal spring of natural length 20.0 cm fixed to the ceiling such that the bottom end is at a height of 30.0 cm from the ground.
(a) When the box of mass 5.00 kg hangs in equilibrium, the bottom end of the spring is at a distance of 25.0 cm from the ground. Determine the spring constant of the spring.
Qns type 2
Daniel decides to have his first attempt at bungee jumping. He falls from rest from the top of a tall cliff with an elastic rope tied to his feet. The force constant of the rope is 100 N m-1, and the rope's unstretched length is 20.0 m. Daniel's mass is 80.0 kg. Assume that the average drag force by the air on Daniel during his jump is 300 N, and that g = 10 m s-2.
(a) Determine the lowest height H Daniel reaches in his jump.
For elasticity, I am not very sure when to apply E=1/2kx^2 and F=kx where x is the extension of the spring. Apparently for qns 1, I should apply F=kx but for qns 2 we should use E=1/2 kx^2. Both qns shows an extension of the spring or rope so therefore I am confused. Pls help thanks!
For qn 1a) ,
Use tension = weight,
kx=mg, solve for k. The answer is 981Nm-1, yes?
F=kx is the equation that relates force and extension
1/2kx^2 = elastic potential energy.
For qn 2a), please double check the question, and let me know if is there a value given for Height, or not.
To solve 2a) , you need a given value for height of cliff, or maximum stretch length of rope, or t, or the value of final velocity v,just before the instantaneous v=0 at the lowest point of his trajectory.
for Q2a, the bungee rope part is actually similar to a past year tys question from H1 Physics 2010 P2. Many students were stuck at this question.
*My personal opinion is that the English of this question is a little weird, probably set by your school teacher. But it is a valid question. However, the intention of the question is excellent.*
Basically, it's a conservation of energy question. I assume for your question, there is a diagram, and the bungee rope was slack, and tied to the top of the building.
Between the top of the building and the lowest point of the motion, there is a loss in GPE but a gain in EPE. Also, consider that unstretched length of bungee rope is 20m, so the initial 20m of fall, there is no gain in EPE. In addition, there are losses of energy to do work against the drag force.
By conservation of energy,
Loss in GPE = Gain in EPE + WD against air resistance
mgH = 0.5 k (H - 20) ^2 + 300H
800H = 50 (H^2 - 40H + 400) + 300H
16H = H^2 - 40H + 400 + 6H
H^2 - 50H + 400 = 0
Solving, H = 40 m or 10 m (reject 10 because H must be larger than 20 m, the unstretched length)
Hi Eagle, i sincerely thank you so much for your guidance + solution. I've learn alot from your input, many others would too, I'll believe.
I hope i can improve on it a little :
H should be defined as : distance from top(at the ceiling) to lowest point of trajectory
(H - 20) should be defined as extension of rope or vertical distance person has travelled(From point of slack rope)
This would allow the statement ' H must be larger than 20m, the unstretched length of rope' , to make more sense.
So the length from ceiling to lowest point of trajectory is 40m,
The (max)extension of rope or (furthest)vertical distance travelled by person is 20m. (when Loss in GPE is fully converted )
The original's question " determine the lowest height H he reaches in his jump " cannot be determined as the whole height from top of ceiling to ground was not given, nor the distance from rope to ground was given.
* assuming "lowest height H he reaches in his jump" means distance relative to the ground.
If it means lowest height H relative to the ceiling, then it's furthest height H from the ceiling, which is 40m.
(I do not think it's possible/able to solve distance from ceiling to ground from the given data?)
Sincere and heartfelt thanks for these friendly and healthy discussion, and your guidance , Eagle !
Hi Flying grenade,
it is only possible to solve the furthest distance reached after falling from the top of the cliff.
Which is why I mentioned the English sounds weird and there's probably a diagram showing information that we do not have :)
Thank you, Eagle !! (:
Added a few more questions for students to try:
(a) Determine the furthest distance that Daniel reached in his fall.
(b) Determine the distance that Daniel has fallen when he reached a maximum speed.
(c) Hence, determine the maximum speed.
(d) Draw an energy distance graph, showing the relationship between EPE, GPE and KE on the same graph, from the point of fall to the furthest distance that Daniel reached in his fall.
No one tried?
Taking g = 9.81,
(a) 39.6 m
(b) 24.8 m
(c) 16.5 m/s