***urgently need these questions to be addressed***
Further questions i have regarding motion in a circle.
I have a question on sth like a ferris wheel. It says the
machine moves at a constant speed in a vertical circle. I thought
when moving in a vertical
circle, speed is always changing since the
direction and magnitude of the forces acting on the body are
varying continuously? How can it have constant speed?
2. Let's say at the top of the ferris wheel, the people inside
the cage will be inverted, give a reason why the person remains on
the floor of the cage.
The reason I always find is that the centripetal acc >
acceleration due to free fall. But why is this so? how does having
a greater centripetal acc than acc due to g prevent the person/obj.
from falling out of the cage?
3.let's say u want to roll a ball up a loop from the bottom.
one of the criteria is for the KE (intial, at the bottom) to be
greater/equal to KE + PE at the top of the loop. How does this
ensure the ball can complete the loop w/o leaving the track at the
max. height? dont underrstand the rationale behind this (i believe
this is almost the same explanation as for question 2)
1) Centripetal force act only to change the
direction of the velocity. It does nothing to change the magnitude
of the velocity.
Hence, the speed remain constant, since speed is only the
magnitude.
As for why the speed can remain constant in a vertical circular
motion, it depends on the question itself.
2) Reaction force from the base of the cage will add on to the
centripetal force.
Draw the free body diagram of the a person in such a situation.
You will find that the only forces are mg and R, and both point
downwards.
In this case, R + mg = centripetal force
The person doesn't fall down because all of the mg is being used
to move him in circular motion instead of accelerating him
downwards.
At the bottom of the circular motion, the free body diagram
changes. R is upwards while mg is downwards. Since centripetal
force is still towards the centre of the circle, R - mg =
centripetal force
3) Yes, same as Q2.
Since centripetal force is proportional to velocity squared, to
require a large enough centripetal force, u need to have a large
enough speed. To ensure that at the max height, u still stay in
contact with the loop, ur centripetal force at that point = g
So you can find the v required at the max height, and hence KE
at max height
To find initial KE, u need to take into account gravitational
forces, which will be under the topic of work energy power.