Name
Period
Date
Motion in 2&3 Dimensions: WORKSHEET 2
1. A woman rides a carnival Ferris wheel of radius 15 m, completing five turns every
minute.
a. What is the
b. Calculate
c. What is the
d. What is the
period of
her speed.
magnitude and
magnitude and
her motion?
direction of her
direction of her
acceleration at
acceleration at
the highest
the lowest
point?
point?
2. An Earth satellite moves in a circular orbit 640 km above Earth’s surface with a
period of 98.0 min. The radius of the Earth is 6.37  10 6 m .
a. Calculate the speed of the satellite.
b. Calculate the acceleration of the
satellite.
3. During an Olympic bobsled run, the Jamaican team makes a turn of radius 7.6 m at
a speed of 96.6 km . What is their acceleration in terms of g?
h
2&3 D Motion: Worksheet 2
page 2
4. A roller coaster has a mass of 1200 kg when fully loaded with passengers. As the
car passes over the top of a circular hill of radius 18 m its speed is 11 m .
s
a. Draw a force diagram of the
b. What is the magnitude of the normal
coaster car at the top of the hill.
force acting on the car?
c. Would a rider feel
lighter, heavier, or
normal? Explain.
d. What is the fastest speed the coaster could go and
still remain in contact with the hill? Draw a new force
diagram.
5. The same roller coaster now travels through the bottom of a circular valley of radius
12 m at a speed of 25 m .
s
a. Draw a force diagram of the
b. What is the magnitude of the normal
coaster car at the bottom of the
force acting on the car?
valley.
c. Would a rider feel
lighter, heavier, or
normal? Explain.
d. How many g’s does the rider feel as she travels
through the bottom of the valley? (Divide the
normal force acting on the rider by their weight.)
2&3 D Motion: Worksheet 2
page 3
6. 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
T  1.7 s
m  73 kg
Figure 2
What is the minimum coefficient of static friction necessary to keep the riders from
sliding down the wall when the floor is lowered from point "a" to point "b"? Start with
a force diagram of the rider when he is on the side of the ride.
7. A roller coaster goes around a loop of radius 22 m as in the
diagram. What is the slowest speed the roller coaster can
have and still make it around the loop?
22 m
2&3 D Motion: Worksheet 2
page 4
8. 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?
9. A mass m on a frictionless table is attached to a hanging mass
M by a cord through a hole in the table as in the diagram.
Find the speed with which m must move for M to stay at rest.
Express your answer in terms of M, m, r, and fundamental
constants.
r
m
M