A light spring of spring constant k = 160 N/m rests vertically on the bottom of a large beaker of water. A 5.00 kg block of wood (density D = 700 kg/m3) is connected to the spring, and the block ? spring system is allowed to come to a static equilibrium
To determine the displacement of the equilibrium position of the block-spring system, we need to consider the forces acting on the system.
1. The weight of the block:
The weight of the block can be calculated using the formula:
Weight = mass x acceleration due to gravity
Weight = mass x 9.8 m/s^2
Weight = 5.00 kg x 9.8 m/s^2
2. The buoyant force acting on the block:
The buoyant force is equal to the weight of the water displaced by the block. The volume of water displaced by the block can be calculated using the formula:
Volume = (mass of the block) / (density of water)
Volume = 5.00 kg / (1000 kg/m^3) [assuming the density of water is 1000 kg/m^3]
The buoyant force can then be calculated using the formula:
Buoyant force = (density of water) x (acceleration due to gravity) x (volume)
Buoyant force = 1000 kg/m^3 x 9.8 m/s^2 x (5.00 kg / (1000 kg/m^3))
3. The force exerted by the spring:
The force exerted by the spring is given by Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. The equation can be written as:
Force = (spring constant) x (displacement of the spring)
Force = 160 N/m x (displacement of the spring)
In static equilibrium, the net force on the system must be zero. Therefore, the force exerted by the spring must balance the weight and the buoyant force.
We can set up an equation:
(Force exerted by the spring) + (Weight of the block) - (Buoyant force) = 0
By substituting the formulas for each force into the equation, we can solve for the displacement of the spring.
Once we have the displacement of the spring, we can determine the equilibrium position by knowing the initial position of the bottom of the spring.