Thread: First-order ODE Word Problem (physics-related)

This is for my DE class and I can't seem to figure it out (probably because my physics is a bit rusty).

Anyway:

An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy of force 1/40 times the weight (w = mg) of the object is pushing the object up. Also, water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10N-sec/m. Find the equation of motion of the object.

Originally Posted by BlazingFire

This is for my DE class and I can't seem to figure it out (probably because my physics is a bit rusty).

Anyway:

An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy of force 1/40 times the weight (w = mg) of the object is pushing the object up. Also, water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10N-sec/m. Find the equation of motion of the object.

let the downward direction be positive, g = 10 m/s^2 ...

$\displaystyle F_{net} = mg - \frac{mg}{40} - 10v$

$\displaystyle m\frac{dv}{dt} = \frac{39}{40}mg - 10v$

$\displaystyle \frac{dv}{dt} = 9.75 - 0.1v$


go for it ...