Yes.
Resolving the centripetal along the surface and equating with the frictional force and the weight (In the same direction) gives the required equation...
What I did was:
Let W = weight of vehicle
N = Normal reaction at surface acting on vehicle
F = Frictional force developed and y = coefficient of friction.
x = Angle of inclination
Resolving weight W perpendicular to the surface we have N = W cos x
The frictional force F =...
Hello,
I was browsing a derivation for the relationship between the curvature of horizontal road curves and the angle of elevation/banking. The derivation is shown on page 4 here: http://www.cdeep.iitb.ac.in/nptel/Civil%20Engineering/Transportation%20Engg%201/14-Ltexhtml/nptel_ceTEI_L14.pdf...
Hmm the answer seems right there but its not clicking. Any more hints.
The work done on the hand by mass = average force x distance = (mg/2 x mg/k) ?
Stored energy = Tension x distance = (mg x mg/k) ?
(Which is obviously not good since we know beforehand that the stored energy = work done on...
There would be 3 forces:
1. Force exerted by the wire on the mass (upwards), T
2. Force exerted by the hand on the mass (upwards), F
3. And the weight (downwards), mg
Resultant force = ma
The equation should be this:
mg - T - F = ma ?
This relates to the extension of a uniform cross-section, homogenous, ideal wire which extends within the proportional limit (Hooke's law).
From my understanding, only half of the gravitational potential energy lost when the mass is lowered on the initially un-extended wire, is stored in the...
Oh god yes, i forgot the 9 in the denominator. Well that partial fraction makes the integrand now easier.
I should complete the denominators to the square and use arctan integral?
It will be of the form
\frac {At+B}{1+t^2} + \frac {Ct+D}{7+4t^2} right?
Consequently
For the numerator,
t^2 = (At+B)(7+4t^2) + (Ct+D)(1+t^2)
(4A+C)t^3 + (4B+D) t^2 + (7A+C)t + (7B+D) = t^2
Comparing coefficients of t^2 and comparing constants we get the 2 equations respectively;
4B...
What method do u think would be best to tackle this one? well i chose tan x because with the denominator containing terms squared, i thought i would end up with an arctan case, but the t^2 in the numerator after simplifying makes it harder to achieve the form if not impossible.
Also when t =...
Homework Statement
Well this is part of an integration process, namely:
\int \frac {sin^2x}{4+3cos^2x}dx
Homework Equations
My attempt involved using a u-substitution, namely t = tan x
The Attempt at a Solution
Using t = tan x, sin^2 x = \frac {t^2}{1+t^2} and cos^2 x = \frac...