A solid sphere of mass m = 2.70 g and radius R = 1.00 cm, is attached to one end of a vertical spring. The other end of the spring is fixed to the bottom of a tank filled with a fluid density Pfluid = 1270 kg/m³. The spring has a natural length L = 8.00 cm and a force constant k = 26.0 N/m. The sphere is submerged in the fluid and comes to rest in equilibrium, with the spring stretched by an amount x. (this problem originally said 27 grams but that was corrected to 2.7 g) A. Draw a force diagram and use it to calculate the equilibrium position of the sphere. B. Now, the sphere is pulled down slightly and released. Assuming that the motion of the sphere is a simple harmonic motion, derive the expression for the time period of oscillation. (hint, remember the differential equation for the regular spring problem we did in class.) C. Discuss how the time period of oscillation would change if the density of the fluid is increased.
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
include diagram/drawing
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images