Question

a water balloon launcher uses an elastic band with a spring constant of 115 N/m to use thee launcher you stretch thee band back with a balloon n it the water balloons have a mass of 1.3 kg a) If you stretch the band by 0.8 m, what elastic force will the band exert? b) With the band stretched 0.8 m, how much elastic potential energy is stored in the spring? c) If you release the band, it pushes forward. What is the kinetic energy of the balloon when it reaches the natural length of the band? d) what is the speed of the balloon when it reaches the natural length of the band?

Answer 1

#1

Elastic force on the balloon

F = kx

here we know that

k = 115 N/m

x = 0.8 m

F = 115 N/m (0.8m) = 92 N

#2

Elastic potential energy

$U = \frac{1}{2}kx^2$

$U = \frac{1}{2}(115)(0.8^2)$

U = 36.8 J

#3

By energy conservation

initial kinetic energy = final potential energy

U = KE

$KE = 36.8 J$

#4

as we know that

$KE = \frac{1}{2}mv^2$

$36.8 = \frac{1}{2}(1.3) v^2$

by solving above equation we have

$v = 7.52 m/s$