I reposted this because the other person did it wrong. Please explain and show s
ID: 1590041 • Letter: I
Question
I reposted this because the other person did it wrong. Please explain and show steps clearly especially part c. I will rate five stars. 3. A marble of mass 10 g falling through a tank of liquid experiences a resistive force R proportional to its velocity. Specifically, R =-bv, where b 3.5 x 10-2 kg s-1. The marble is dropped from rest and begins to accelerate downward. (a) What is the marble's terminal velocity in this liquid? (b) How much time elapses before the marble has reached 95% of its terminal velocity? (c) How far does it travel during this time? Please make work legible and clear I want to understand how to do it. Please also only use Newtonian mechanicsExplanation / Answer
a) at terminal velocity,
Fnet on marble = 0
mg - R = 0
mg - bv = 0
v = (10 x 10^-3 x 9.81 ) / (3.5 x 10^-2)
v = 2.80 m/s
b) 95% of terminal velocity
= 0.95 x 2.80 = 2.66 m/s
on marble .
Fnet = m dv/dt = mg - bv
(m / mg-bv)dv = dt
integrating,
- m ln(mg - bv) / b = t
from 0 to 2.66 m/s
- 0.01 [ln (0.01*9.81 - 0.035*2.66) - ln (0.01*9.81)] / 0.035 = t
t = 0.85s
3) - m ln(mg - bv) / b = t
ln(mg - bv) = - bt/m
mg - bv = e^(-bt/m)
v = (mg - e^(-bt/m)) / b
dr/dt = (mg - e^(-bt/m)) / b
integrating,
r = mgt/b + me^(-bt/m) /b^2
r = (0.01 x 9.81 x 0.85 / 0.035) + (0.01 x e^(-0.035x0.85/0.01) / 0.035^2 )
r = 2.80 m