The desperate contestants on a TV survival show are very hungry. The only food t
ID: 2036471 • Letter: T
Question
The desperate contestants on a TV survival show are very hungry. The only food they can see is some fruit hanging on a branch high in a tree. Fortunately, they have a spring they can use to launch a rock. The spring constant is 1300 N/m, and they can compress the spring a maximum of 40 cm. All the rocks on the island seem to have a mass of 480 g.
(a) With what speed does the rock leave the spring?
m/s
(b) To what height can the rock be launched? (Assume the spring's equilibrium length is 50 cm.)
m
If the fruit hangs 15 m above the ground, will they feast or go hungry?
go hungry///feast
Explanation / Answer
(a)
elastic energy stored after compression U = (1/2)*k*x^2
kinetic energy of the stoen after leaving the spring K = (1/2)*m*v^2
from energy relation
K = U
(1/2)*m*v^2 = (1/2)*k*x^2
speed v = x*sqrt(k/m)
x = maximum compression = 0.4 m
K = 1300 N/m
speed v = 0.4*sqrt(1300/0.48)
speed v = 20.8 m/s
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b)
at the maximum height gravitational potential energy Ug = m*g*h
Ug = K
m*g*h = (1/2)*m*v^2
maximum height h = v^2/(2g) = 22.1 m
height reached = h + 0.5 = 22.6 m
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15 < 22.6
they will feast