If we are in the frame of a pendulum (accelerating frame) it will have a centrifugal force and it's weight acting vertically downwards and the tension of the string acting vertically upwards. Now the force equation will be $$T=mg+\frac{mv^2}{R}$$(T=tension | m=mass of pendullum | v=velocity at its lowest point on the circle | R is the length of string(radius of circular motion)…
Now these forces are balanced in magnitude and opposite in direction so wouldn't the net force at the bottom be$=0$ and the net acceleration$=0$ at the bottom of the circular motion as a result?
(There are no others forces acting to give it an acceleration hence why the net acceleration not$=0$?)
this is the problem where in the solution it is considered that the bob has acceleration of $\frac{v^2}{R}$
at the bottom most point and not zero.How can this be explained??(https://i.stack.imgur.com/CNAXQ.jpg)
Solution to the above problem
(https://i.stack.imgur.com/ajj5O.jpg)
Best Answer
The drawing is incorrect. If the forces on the pendulum bob were balanced, there would be no net force on the pendulum bob, and its direction of motion at the bottom of the arc would be tangential to the circle (e.g., horizontal).
"Centripetal force" is a catchall term for some force that is causing circular motion. In this case, centripetal force is being caused by tension in the string. This means that "T" should be shown on the drawing to represent tension in the string, but centripetal force should NOT be shown on the drawing. Naturally, this leads to the following equation when the pendulum bob is at the bottom of the arc:
$T = \frac{mv^2}{r} + mg$
which means that the maximum force on the string occurs when the pendulum bob is at the bottom of the arc, and this force is pointing towards the center of the circle that the pendulum bob is swinging through.