Answer:
![\boxed{\sf Viscosity \ of \ glycerine \ (\eta) = 14.382 \ poise}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Csf%20Viscosity%20%5C%20of%20%5C%20glycerine%20%5C%20%28%5Ceta%29%20%3D%2014.382%20%5C%20poise%7D%20)
Given:
Radius of ball bearing (r) = 1.5 mm = 0.15 cm
Density of iron (ρ) = 7.85 g/cm³
Density of glycerine (σ) = 1.25 g/cm³
Terminal velocity (v) = 2.25 cm/s
Acceleration due to gravity (g) = 980.6 cm/s²
To Find:
Viscosity of glycerine (
)
Explanation:
![\boxed{ \bold{v = \frac{2}{9} \frac{( {r}^{2} ( \rho - \sigma)g)}{ \eta} }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7Bv%20%3D%20%20%5Cfrac%7B2%7D%7B9%7D%20%20%5Cfrac%7B%28%20%7Br%7D%5E%7B2%7D%20%28%20%5Crho%20-%20%20%5Csigma%29g%29%7D%7B%20%5Ceta%7D%20%7D%7D)
![\sf \implies \eta = \frac{2}{9} \frac{( {r}^{2}( \rho - \sigma)g )}{v}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%20%5Cfrac%7B2%7D%7B9%7D%20%20%5Cfrac%7B%28%20%7Br%7D%5E%7B2%7D%28%20%5Crho%20-%20%20%5Csigma%29g%20%29%7D%7Bv%7D%20)
Substituting values of r, ρ, σ, v & g in the equation:
![\sf \implies \eta = \frac{2}{9} \frac{( {(0.15)}^{2} \times (7.85 - 1.25) \times 980.6)}{2.25}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%20%5Cfrac%7B2%7D%7B9%7D%20%20%5Cfrac%7B%28%20%7B%280.15%29%7D%5E%7B2%7D%20%20%5Ctimes%20%20%287.85%20-%201.25%29%20%5Ctimes%20980.6%29%7D%7B2.25%7D%20)
![\sf \implies \eta = \frac{2}{9} \frac{(0.0225 \times 6.6 \times 980.6)}{2.25}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%20%5Cfrac%7B2%7D%7B9%7D%20%20%5Cfrac%7B%280.0225%20%5Ctimes%206.6%20%5Ctimes%20980.6%29%7D%7B2.25%7D%20)
![\sf \implies \eta = \frac{2}{9} \times \frac{145.6191}{2.25}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%20%5Cfrac%7B2%7D%7B9%7D%20%20%5Ctimes%20%20%5Cfrac%7B145.6191%7D%7B2.25%7D%20)
![\sf \implies \eta = \frac{2}{9} \times 64.7196](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%20%5Cfrac%7B2%7D%7B9%7D%20%20%5Ctimes%2064.7196)
![\sf \implies \eta = 2 \times 7.191](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%202%20%5Ctimes%207.191)
![\sf \implies \eta = 14.382 \: poise](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Ceta%20%3D%20%2014.382%20%5C%3A%20poise)
Answer:
each resistor is 540 Ω
Explanation:
Let's assign the letter R to the resistance of the three resistors involved in this problem. So, to start with, the three resistors are placed in parallel, which results in an equivalent resistance
defined by the formula:
![\frac{1}{R_e}=\frac{1}{R} } +\frac{1}{R} } +\frac{1}{R} \\\frac{1}{R_e}=\frac{3}{R} \\R_e=\frac{R}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BR_e%7D%3D%5Cfrac%7B1%7D%7BR%7D%20%7D%20%2B%5Cfrac%7B1%7D%7BR%7D%20%7D%20%2B%5Cfrac%7B1%7D%7BR%7D%20%5C%5C%5Cfrac%7B1%7D%7BR_e%7D%3D%5Cfrac%7B3%7D%7BR%7D%20%5C%5CR_e%3D%5Cfrac%7BR%7D%7B3%7D)
Therefore, R/3 is the equivalent resistance of the initial circuit.
In the second circuit, two of the resistors are in parallel, so they are equivalent to:
![\frac{1}{R'_e}=\frac{1}{R} +\frac{1}{R}\\\frac{1}{R'_e}=\frac{2}{R} \\R'_e=\frac{R}{2} \\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BR%27_e%7D%3D%5Cfrac%7B1%7D%7BR%7D%20%2B%5Cfrac%7B1%7D%7BR%7D%5C%5C%5Cfrac%7B1%7D%7BR%27_e%7D%3D%5Cfrac%7B2%7D%7BR%7D%20%5C%5CR%27_e%3D%5Cfrac%7BR%7D%7B2%7D%20%5C%5C)
and when this is combined with the third resistor in series, the equivalent resistance (
) of this new circuit becomes the addition of the above calculated resistance plus the resistor R (because these are connected in series):
![R''_e=R'_e+R\\R''_e=\frac{R}{2} +R\\R''_e=\frac{3R}{2}](https://tex.z-dn.net/?f=R%27%27_e%3DR%27_e%2BR%5C%5CR%27%27_e%3D%5Cfrac%7BR%7D%7B2%7D%20%2BR%5C%5CR%27%27_e%3D%5Cfrac%7B3R%7D%7B2%7D)
The problem states that the difference between the equivalent resistances in both circuits is given by:
![R''_e=R_e+630 \,\Omega](https://tex.z-dn.net/?f=R%27%27_e%3DR_e%2B630%20%5C%2C%5COmega)
so, we can replace our found values for the equivalent resistors (which are both in terms of R) and solve for R in this last equation:
![\frac{3R}{2} =\frac{R}{3} +630\,\Omega\\\frac{3R}{2} -\frac{R}{3} = 630\,\Omega\\\frac{7R}{6} = 630\,\Omega\\\\R=\frac{6}{7} *630\,\Omega\\R=540\,\Omega](https://tex.z-dn.net/?f=%5Cfrac%7B3R%7D%7B2%7D%20%3D%5Cfrac%7BR%7D%7B3%7D%20%2B630%5C%2C%5COmega%5C%5C%5Cfrac%7B3R%7D%7B2%7D%20-%5Cfrac%7BR%7D%7B3%7D%20%3D%20630%5C%2C%5COmega%5C%5C%5Cfrac%7B7R%7D%7B6%7D%20%3D%20630%5C%2C%5COmega%5C%5C%5C%5CR%3D%5Cfrac%7B6%7D%7B7%7D%20%2A630%5C%2C%5COmega%5C%5CR%3D540%5C%2C%5COmega)
Answer:
67.9 kg*m/s
Explanation:
Pi = 38 kgm/s
F = 88.3N and ∆t = 0.338s
Final momentum Pf = Pi + F∆t = 38 + (88.3)(0.338) = 38 + 29.8454
=) Pf = 67.8454 kgm/s = 67.85kg*m/s
Your answer is 67.9kg*m/s with three significant figures
hope this helps your troubles!
Physical science is the study, measurement and observation of nonliving objects whereas biological.