Name
Period
Date
Central Force Worksheet 2
1. A woman flying aerobatics executes a maneuver as illustrated in Figure 1 below:
r
r  3.8  10 2 m
v  65.3 m
s
m w  55 kg
Figure 1
a. Construct a quantitative diagram of all relevant forces acting on the woman
flying the airplane when at the top of the loop, as indicated in Figure 1.
b. What is the slowest speed she could travel and not fall out of her seat? Draw a
force diagram of the woman at that speed.
Central Force Worksheet 2
page 2
2. A popular amusement park ride, Figure 2, operates as follows: riders enter the
cylindrical structure when it is stationary with the floor at the point marked "a". They
then stand against the wall as the cylinder then begins to rotate. When it is up to
speed, the floor is lowered to the position marked "b", leaving the riders
"suspended" against the wall high above the floor.
r  1. 5 m
 s  0.50
m  73 kg
Figure 2
a. What is the slowest speed necessary to keep the riders from sliding down the
wall when the floor is lowered from point "a" to point "b"? (Show all of your work
and explain your reasoning.) Start with a force diagram of the rider when he is
on the left hand side of the ride.
b. What is the longest period of rotation necessary to keep the riders from sliding
down the wall?
Central Force Worksheet 2
page 3
3. A 1300 kg car is rounding a curved stretch of road of radius 29 m at the fastest
constant speed that it can travel and not slip off of the road. The coefficient of static
friction between the car and the road is 0.79 .
a. Draw a force diagram of the car.
b. What force of static friction is
Consider the car to be coming
needed to keep the car from sliding
out of the page and rounding the
off the road?
curve to your right.
c. What is the fastest speed the car
could travel and not slip off of the
road?
d. At what angle would the road need
to be banked so the car could
traverse it at the same speed but
without the aid of friction?
4. A certain string can withstand a maximum tension of 40. N (the test of the string)
without breaking. A child ties a 0.367 kg stone to one end and, holding the other
end, whirls the stone in a vertical circle of radius 0.91 m , slowly increasing the speed
of the stone until the string breaks.
a. Where is the stone in its path when the string breaks? Explain why.
b. What is the speed of the stone as the string breaks? Draw a force diagram of
the stone just before the string breaks.