First, volume displaced:
ρV = m ==> ρ/m = V
Where ρ is density, V is volume, m is mass
The block pushes down with a force equal to its weight, 8kgf. Since
force =-kx for a spring, when the pool is filled, it lifts with a
force of 16kgf against the spring. So, it must displace 92kg of
water, because it must lift 16kgf for the spring force, and 16kgf
for its own weight.
ρ∙V = m ==> ρ/m = V
total water V = ρ/m = 1000kg/m³ / 92kg = 10.868m³
wood V = ρ/m = 850kg/m³ / 8kg = 106.25m³
void V = ΔV = 106.25m³ - 10.868m³ = 85.38m³
% hollow = Vvoid/ Vtotal = 0.0452m³ / 0.075m³ = 60.3%
I use gravimetric units [kgf], which is not strictly allowed for
SI; use mg = W instead of kgf.
A spring is attched to the bottom of an empty swimming pool, with axis ot the...
A light spring of constant 177 N/m rests vertically on the bottom of a large beaker of water. A 4.42 kg block of wood of density 669 kg/m3 is connected to the top of the spring and the block-spring system is allowed to come to static equilibrium. What is the elongation ∆L of the spring? The acceleration of gravity is 9.8 m/s 2 . Answer in units of cm.