Final

Final Finally...

Median: 70-80%S.D. 20%

○ This means there was a huge spread of scores (34%-98% without outliers)

But a histogram shows a lot of high scores and no downward turn at the high end(a first)

So... What worked?What didn’t?

Student scores05

10152025303540

20-30%30-40%40-50%50-60%60-70%70-80%80-90%90-100%

CIRCULAR MOTIONThings that go round and round and round… part 2

Could be worse…

Everyday Application after Finals A person has a mass of 65kg. The harness is

attached to a 45m “special” rope swing. They then lean step off of a bridge. When (consider the path they will take) will the net

force on the swingers be at its greatest? Explain.They experience a maximum centripetal force of

1150N, how fast are they traveling at this point?What is the centripetal force on them at the top of

the swing’s path? Explain. Swing

Think you’ve got it eh? Consider the following clip and explain

the motion of your body during the ride. Hold On To Your Seat!

Centripetal Force Centripetal force is not a REAL force,

rather it is just another way of saying net force when describing an object with circular motion.

So what is the net force on the ride? What is the Tension compared to the

person’s weight?

What is the direction of the NET force? The weight is equal to FT cosq.

Note this is different than sliding! The Fcentripetal is equal to FT sinq.

FT sinq = mv2/r What does the Tension equal? FT cosq = mg so FT = mg / cosq

Also:

FT

FW

FW

Fc

q

so… tanq = v2/gr and q = tan-1 (v2/gr)

FT sinq mv2/rFT cosq mg

=tanq = the masses cancel!

Why Bank the Turn? Who Needs a Bank? Draw the FBD of the luge

guy on a banked turn. Which way is the net

force? Which way is the

centripetal force? Which way is he

accelerating?

Details! What is the direction of the NET force? The weight is equal to FNcosq. The Fcentripetal is equal to FNsinq. The same relationship as the circular

swing.

Practice If we wanted to make a road for a car that

had a 65m radius turn and the speed limit was 40mph (18m/s), what should the angle of the bank be to avoid sideways friction?

Velodrome

The angle of bank at the Velodrome is 27 ͦ. One lap is 333.3m and has a radius of 23.m on the corners. At what speed was it designed for and what is your apparent weight in the turn?

11m/s, about 24mph, Your apparent weight is 1.12x your normal weight

The same technique applies to skiers and skaters who must lean to make a turn.

The more leaning into a turn, the larger the net force, and the smaller radius of a turn you’ll

make.

If the velocity of Herr Maier is 20.m/s and the angle is 18º , what is the radius of this turn?

What is the force on his outside leg if his mass is 85kg?

If the fuzzy dice have an angle of 12º from vertical as the car goes around the turn, what is the centripetal acceleration? What is the friction force on your physics friend to stay in the seat?

(He weighs 75kg)