Question

Resistive Force Proportional to Velocity -objects falling through a fluid -small objects (dust particles) in air. Resistive Force D = -bv v: velocity of object b: constant which depends on medium and on shape of object. For a sphere b ~ r. (kg/s) Consider dropping a sphere of mass m in a fluid. Forces which act: mg = weight (corrected for buoyant force) -bv = resistive force. Applying Newton's Second Law ?Fy = may mg - bv = m(dv/dt) This is a so-called differential equation a = dv/dt = g - b/m v

          Resistive Force Proportional to Velocity
-objects falling through a fluid
-small objects (dust particles) in air.
Resistive Force D = -bv
v: velocity of object
b: constant which depends on medium and on shape of object. For a sphere b ~ r. (kg/s)
Consider dropping a sphere of mass m in a fluid.
Forces which act:
mg = weight (corrected for buoyant force)
-bv = resistive force.
Applying Newton's Second Law
?Fy = may
mg - bv = m(dv/dt) This is a so-called differential equation
a = dv/dt = g - b/m v

Resistive Force Proportional to Velocity
-objects falling through a fluid
-small objects (dust particles) in air.
Resistive Force D = -bv
v: velocity of object
b: constant which depends on medium and on shape of object. For a sphere b r. (kg/s)
Consider dropping a sphere of mass m in a fluid.
Forces which act:
mg = weight (corrected for buoyant force)
-bv = resistive force.
Applying Newton's Second Law
?Fy = may
mg - bv = m(dv/dt) This is a so-called differential equation
a = dv/dt = g - b/m v

Added by Leslie D.

Essential University Physics

Richard Wolfson 3rd Edition

Chapter 5

Instant Answer

Solved by Expert Sachin Rao

03/04/2021

Step 1

- Given velocity function: \( v(t) = \frac{mg}{b} \left(1 - \exp\left(-\frac{bt}{m}\right)\right) \) - Given differential equation: \( \frac{dv(t)}{dt} = g - \frac{b}{m} v(t) \) Show more…

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