A block of mass 0.65 kg and density 650 kg/m³ is forced under the surface of the water by means of a spring (k = 60.0 N/m) that is fixed to the bottom of the container as shown in the figure. How much is the spring stretched? (the density of water is 1000 kg/m³).
To find how much the spring is stretched, we need to calculate the difference in buoyant force and the force exerted by the spring. Let's break down the solution into steps:
Step 1: Calculate the weight of the block
The weight of the block can be found by multiplying its mass (m) by the acceleration due to gravity (g):
Weight (W) = m * g
Given: mass (m) = 0.65 kg, g = 9.8 m/s²
Calculate the weight of the block.
Step 2: Calculate the buoyant force
The buoyant force (F_b) is equal to the weight of the water displaced by the block. It can be calculated using Archimedes' principle:
F_b = Density of water * Volume of the block * g
Given: Density of water = 1000 kg/m³, Volume of the block = (mass of the block) / (density of the block)
Calculate the buoyant force.
Step 3: Calculate the force exerted by the spring
The force exerted by the spring (F_s) can be calculated using Hooke's law:
F_s = k * x
Given: spring constant (k) = 60.0 N/m
We need to find the spring stretch (x), which is the unknown in this question.
Step 4: Equilibrium condition
In equilibrium, the force exerted by the spring (F_s) is equal to the net force. The net force is the difference between the weight of the block (W) and the buoyant force (F_b):
F_net = W - F_b
Since the block floats, the net force is zero in equilibrium:
F_net = 0
Setting the net force equation to zero, we can solve for the spring stretch (x):
0 = W - F_b = k * x
Rearranging the equation, we get:
x = (W - F_b) / k
Calculate the spring stretch (x) using the weight of the block (W) and the buoyant force (F_b) calculated in previous steps.
Follow these steps to find the answer.