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Answer:
Compression of the spring: 0.18 m (downward)
Explanation:
The forces acting on the block of wood are:
- The force of gravity, acting downward, of magnitude , where m = 5.32 kg is the mass of the block and
is the acceleration due to gravity
- The force exerted by the spring, downward, of magnitude , where
is the spring constant and
is the elongation of the spring
- The buoyant force, upward, of magnitude , where
is the water density and V the volume of the block
Since the block is in equilibrium, the net force is zero, so we can write
(1)
We have to find the volume of the block first. We have:
m = 5.32 kg (mass)
(wood density)
So, the volume is
So now we can re-arrange eq.(1) to find the elongation of the spring, x:
So, the spring is compressed by 0.18 m.