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Since the car is turning on a curve, The car will be accelerating as direction of the car changes even the velocity is constant. This acceleration is centripetal acceleration And centripetal force will be providing it,
There are three cases with turning
1) Unbanked curve.
2) Banked curve with no friction
3) Banked curve with friction
Mechanics of Turning a car on the curve Read More »
For integration of $\log(\tan x)$, we generally consider the definite integral over the interval from 0 to $\pi/2$ To calculate the definite integral of $\log(\tan x)$ from (0) to $\pi/2$, we use a technique involving symmetry and the properties of logarithms. The integral is: \[\int_{0}^{\pi/2} \log(\tan x) \, dx\] Let $I=\int_{0}^{\pi/2} \log(\tan x) \, dx$
Integration of log tanx Read More »
For integration of $\log(\cos x)$, we generally consider the definite integral over the interval from 0 to $\pi/2$ To calculate the definite integral of $\log(\cos x)$ from (0) to $\pi/2$, we use a technique involving symmetry and the properties of logarithms. The integral is: \[\int_{0}^{\pi/2} \log(\cos x) \, dx\] Let $I=\int_{0}^{\pi/2} \log(\cos x) \, dx$
integration of log cosx Read More »
The integral ($\int e^{ax} \sin(bx) \, dx$) is computed as: \[\int e^{ax} \sin(bx) \, dx= \frac{a e^{ax} \sin(bx)}{a^2 + b^2} – \frac{b e^{ax} \cos(bx)}{a^2 + b^2}+ C\] Proof of Integration To solve the integral $\int e^{ax} \sin(bx) \, dx$, we can use the method of integration by parts, which is based on the formula: $$\int
integration of e^{ax} sin bx Read More »
The integration of a periodic function involves some unique properties and approaches due to the function’s repeating nature. A function $f(x)$ is said to be periodic with period $T$ if for all $x$ in the domain of $f$, $f(x + T) = f(x)$. This periodicity can significantly simplify the integration process over intervals that are
Integration of periodic functions Read More »
This can be done in these simple steps
1) First draw a free body diagram of the body showing all the forces on it.
2) Carefully choose a X-Y coordinate system so that direction of the motion or direction of force lies in X or Y direction. This will simplfy the Problem
3) Applying Newton’s law find out any unknown forces
How to find work done by Multiple forces acting on a object Read More »
For one dimensional motion, the force can be found from Potential energy using following formula
How to Calculate the force given potential energy Read More »
Two most common errors you should avoid when you see an average speed question.
Mistake #1
The most common mistakes in average speed problems occurs when the question asks you to calculate the average speed of a object moving at two different speeds for different parts of the journey. Students are generally tempted to calculate the arithmetic mean (average) of the two speeds, and select a corresponding answer. This averaging approach is wrong.
Common mistake doing average speed calculation Read More »
