Solving Circular Motion Qs: Flea on a Record & Pilot in a Loop

[crosbykins]

URGENT: circular motion qs

Homework Statement

1. A 0.20g flea sits at a distance of 5.0cm from the centre of a rotating record.
a) If the record rotates at 77rpm, what is the centripetal force.
b) For the flea to remain at this spot, what must be its frictional force?

2. A pilot of mass 60.0kg is flying her plane in a vertically oriented circular loop. Just at the bottom of the loop, the plane's speed is 1.8*10^2km/h and the pilot feels exactly four times as heavy as she normally does.
a) What is the radius of the loop.
b)At what speed must she be flying at the top of the loop in order to feel weightless?

Homework Equations

Fnet = 4pi^2mrf^2
Fnet = mv^2/r

The Attempt at a Solution

a)
77rpm * (1/60s)
=1.3s^-1

Fnet=4pi^2(.0002kg)(.005m)(1.3s^-1)^3
=6.7*10^-5N

Therefore, the centripetal force is 6.7*10^-5N

b)
For the flea to stay in the same spot the firction must be 6.7*10^-5N also.

2.
a)
4mg = mv^2/r
r = v^2/4mg
=64m

Therefore, the radius is 64m.

b)
mg=mv^2/r
[(60.0kg)(9.8m/s^2)(64m)]/60.0kg =v^2
25m/s=v

Therefore, she must be flying at a speed of 25m/s.

 

[gneill]

There's no question; Can't be all that urgent!

 

[crosbykins]

There's no question; Can't be all that urgent!

It's urgent because i think i did it all wrong...

 

[gneill]

In the first question I think one problem stems from rounding intermediate results. Leave some more digits on the frequency that you calculated (it's an intermediate value -- part of the process, not the end result) round results to the required significant figures. You've also got a problem with your conversion of cm to m for the radius -- check the order of magnitude.

For the second question you need to pay attention to what forces are acting when. In particular, at the bottom of the loop the centripetal force due to the plane's motion is acting as well as the force due to gravity.

 

[crosbykins]

In the first question I think one problem stems from rounding intermediate results. Leave some more digits on the frequency that you calculated (it's an intermediate value -- part of the process, not the end result) round results to the required significant figures. You've also got a problem with your conversion of cm to m for the radius -- check the order of magnitude.

For the second question you need to pay attention to what forces are acting when. In particular, at the bottom of the loop the centripetal force due to the plane's motion is acting as well as the force due to gravity.

for part b of qs 2, isn't the pilot experiencing weightlessness so the Fn would be 0 and the only other force is Fgrav?

 

[gneill]

If the net force is zero, then the sum of all forces is zero.

 

[crosbykins]

If the net force is zero, then the sum of all forces is zero.

this is really confusing, is it possible you write write out a step-by-step solution only to 2. b)? if not it's ok, thanks for the help

 

[crosbykins]

If the net force is zero, then the sum of all forces is zero.

i meant Fnormal is 0, so the only force acting on the pilot when she is at the bottom is gravity

 

[gneill]

If the plane is flying in a circular loop, then centripetal force will always be acting. Gravity, too, is always acting. The only difference between the top and bottom of the the loop is the relative directions of these forces, and, of course, the magnitude of the centripetal force if the velocity changes.

Draw free body diagrams for the forces in each case. Then do the sums.