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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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