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

Answer 1

(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

----------------------

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

==========================

15 < 22.6

they will feast