Answer to Question #101132 in Physics for Tosin

Question

A frog with the mass 30 g rests on the little wooden square float with square 100 cm2 and height 5 cm. How high shall the frog jump in order to make a float sink into the water completely. The water density is 1000 kg/m3, The wood density is 740 kg/m3. Please present the result in meters, rounded up to 3 significant digits.

Answer 1

From the conservation of energy:

$$mgH=W$$

$$F_{net} =(\rho_w-\rho)gAy$$

$$W(y)=0.5(\rho_w-\rho)gAy^2$$

$$W=W(h)=0.5(\rho_w-\rho)gAh^2$$

So,

$$mgH=0.5(\rho_w-\rho)gAh^2\to mH=0.5(\rho_w-\rho)Ah^2$$

$$(0.03)H=0.5(1000-740)(0.01)(0.05)^2$$

$$H=0.108\ m$$