Standard +0.8 This is a multi-step energy conservation problem requiring careful consideration of three phases (free fall, elastic extension, and air resistance throughout). Students must set up and solve a quadratic equation involving gravitational PE, elastic PE, and work against resistance. While the method is standard for Further Mechanics, the bookkeeping and algebraic manipulation elevate it above routine difficulty.
2 A bungee jumper of mass 80 kg steps off a high bridge with an elastic rope attached to her ankles. She is assumed to fall vertically from rest and the air resistance she experiences is modelled as a constant force of 32 N . The rope has natural length 4 m and modulus of elasticity 470 N .
By considering energy, determine the total distance she falls before first coming to instantaneous rest.
Energy lost (work done by air resistance) =32(x+4)
470x2
80g(x+4)= +32(x+4)
2×4
235x2−3008x−12032=0 soi
x = 16
Answer
Marks
She falls 20 m before first coming to rest
M1
M1
M1
A1
M1
A1
Answer
Marks
[6]
3.3
3.3
3.3
3.4
1.1
Answer
Marks
2.3
Attempt GPE
Attempt EPE
Attempt Work done
Initial energy = Final Elastic
PE + energy lost
Can be multiple of this
Only from W-E principle
with three terms
Answer
Marks
–3.2 rejected
Or 80gd where d is the distance
below the bridge
470(d−4)2
2×4
470(d−4)2
80gd = +32d
8
235d2−4888d+3760=0
d = 20 (and 0.8 rejected)
Question 2:
2 | Initial energy = 80g(x + 4) where x is the final
extension of the rope
470x2
Elastic PE =
2×4
Energy lost (work done by air resistance) =32(x+4)
470x2
80g(x+4)= +32(x+4)
2×4
235x2−3008x−12032=0 soi
x = 16
She falls 20 m before first coming to rest | M1
M1
M1
A1
M1
A1
[6] | 3.3
3.3
3.3
3.4
1.1
2.3 | Attempt GPE
Attempt EPE
Attempt Work done
Initial energy = Final Elastic
PE + energy lost
Can be multiple of this
Only from W-E principle
with three terms
–3.2 rejected | Or 80gd where d is the distance
below the bridge
470(d−4)2
2×4
470(d−4)2
80gd = +32d
8
235d2−4888d+3760=0
d = 20 (and 0.8 rejected)
2 A bungee jumper of mass 80 kg steps off a high bridge with an elastic rope attached to her ankles. She is assumed to fall vertically from rest and the air resistance she experiences is modelled as a constant force of 32 N . The rope has natural length 4 m and modulus of elasticity 470 N .
By considering energy, determine the total distance she falls before first coming to instantaneous rest.
\hfill \mbox{\textit{OCR Further Mechanics 2020 Q2 [6]}}