What Causes the Net Force on a Displaced Ship in SHM?

  • Thread starter Thread starter crossfacer
  • Start date Start date
  • Tags Tags
    Floating Shm
Click For Summary
SUMMARY

The net force acting on a displaced ship in simple harmonic motion (SHM) is defined by the equation F = -d g A y, where d represents the density of water, g is the acceleration due to gravity, A is the cross-sectional area of the ship, and y is the additional depth the ship is displaced. The weight of the ship, Mg, is balanced by the buoyant force when the ship is floating at equilibrium. When the ship is displaced further into the water, the net force is derived from the difference between the weight of the displaced water and the weight of the ship, leading to the conclusion that the buoyancy force adjusts to maintain equilibrium.

PREREQUISITES
  • Understanding of buoyancy principles and Archimedes' principle
  • Basic knowledge of simple harmonic motion (SHM)
  • Familiarity with forces, mass, and density calculations
  • Knowledge of gravitational acceleration (g) and its implications
NEXT STEPS
  • Study Archimedes' principle in-depth to understand buoyancy forces
  • Explore the mathematical derivation of simple harmonic motion equations
  • Learn about the relationship between mass, volume, and density in fluid mechanics
  • Investigate the effects of varying cross-sectional areas on buoyancy and stability
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and fluid dynamics, as well as educators seeking to explain concepts of buoyancy and simple harmonic motion.

crossfacer
Messages
20
Reaction score
0

Homework Statement


There is a ship of mass M floating on a river. The upper portion of the ship has a uniform cross-sectional area A and the density of water is d. Now the ship is displaced a further depth y into the water and released.
What is the resultant force acting on the ship when it is displaced a further depth y into the water?

The Attempt at a Solution


d = m / v where m is the mass of water and v is volume of water being pushed by ship
m = d (A*y)
net F= Mg - mg
net F= g [ M - d (A*y) ]The correct answer is F= - dgAy. Why isn't the weight of the ship taken into account?
Thank you so much!
 
Physics news on Phys.org
The ship is floating on the river. So the buoyancy force for the part of the ship that was below the waterline when y = 0 equals its weight Mg.
 
Initially, F_b=dAy_o where y_o is the intial depth of the ship. The depth of the ship when its pushed down by a length dy (or y) is y_o+dy (or y_o+y)
 

Similar threads

Depth of a basketball floating on water
  • · Replies 9 ·
Replies
9
Views
1K
Ship draft (draught) word problem buoyancy
  • · Replies 3 ·
Replies
3
Views
2K
Motion of a Parachuter (Terminal Velocity, Time of Flight, Distance)
  • · Replies 10 ·
Replies
10
Views
1K
Problem Set Involving Inertia and Balloons
  • · Replies 2 ·
Replies
2
Views
2K
Bernoulli, Fluid Dynamics, and ships
  • · Replies 5 ·
Replies
5
Views
3K
What is the Error Source in SHM Experiment with Floating Cylinder?
  • · Replies 4 ·
Replies
4
Views
5K
Buoyancy: Cube of Iron - solved this correctly?
  • · Replies 1 ·
Replies
1
Views
3K
Hydrostatic Problem: Hinged water gate at the bottom of a reservoir
  • · Replies 3 ·
Replies
3
Views
3K
Does Dropping the Anchor Affect the Barge's Water Displacement?
  • · Replies 20 ·
Replies
20
Views
2K
Volume of water a ship must displace to float
  • · Replies 4 ·
Replies
4
Views
4K