In a non-creepy way, you are hanging out at a playground and happen to observe a
ID: 1530389 • Letter: I
Question
In a non-creepy way, you are hanging out at a playground and happen to observe a child bouncing up and down on a frog on a spring. You notice at one particular instant that the child is 5 cm from the equilibrium position, and moving at 0.4 m/s. You also happen to know that the frog and child together have a mass of 100 kg, and the spring constant of the spring they sit on is 500 N/m.
a. What is the total energy of the child + frog + spring system?
b. What is the amplitude of the vertical motion of the child?
c. What is the maximum speed that the child achieves during this motion?
Explanation / Answer
a) Total energy, E = (1/2)*k*x^2 + (1/2)*m*v^2
= (1/2)*500*0.05^2 + (1/2)*100*0.4^2
= 8.625 J
b) use, E = (1/2)*k*A^2
==> A = sqrt(2*E/k)
= sqrt(2*8.625/500)
= 0.186 m or 18.6 cm
c) Vmax = A*w
= A*sqrt(k/m)
= 0.186*sqrt(500/100)
= 0.416 m/s
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