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Circular Motion
1) A 4 kg ball moves in a circle at a speed of 1.4 m/s. If the rope has a radius 0.62 m and can tolerate a
maximum tension of 45-N, will the string break?
2) A 15 kg ball has a tension of 1500 N when swung in a circle of radius 12 m. What is its velocity at the top
of the circle?
3) You (55 kg) are rounding a large hill (with radius 20 m) of a roller coaster. If your speed is 12 m/s, what
is the normal force of the seat on your butt? (154-N)
4) You (65 kg) are rounding the bottom of a curve (with radius 17 m) of a roller coaster. If your speed is 20
m/s, what is the normal force of the seat on your butt? (2180-N)
5) You (60 kg) are upside down inside of the top of a loop (with radius 15 m) of a roller coaster. If the speed
is 20 m/s, what is the normal force of the seat on your butt? (1000-N)
6) You (60 kg) are rounding the top of a hill (with radius 15 m) of a roller coaster. If the normal force of the
seat on your butt is 500 N, how fast are you going? (5 m/s)
7) You (60 kg) are rounding the bottom of a loop (with radius 15 m) of a roller coaster. If the normal force
of the seat on your butt is 2200 N, how fast are you going? (20 m/s)
8) You (60 kg) are upside down inside of the top of a loop (with radius 15 m) of a roller coaster. If the
normal force of the seat on your butt is 500 N, how fast are you going? (16.6 m/s)
9) You are to design a 20-m radius circular curve of highway so that cars can move along the curve and not
slip, even when the road is icy. What is the maximum speed with which the car can go if the coefficient of
friction is 0.4?
10) You (60kg) sit in the middle of the rough surface backseat of a car. The car rounds a 40-m radius curve
toward the right while moving at a constant speed of 10 m/s. What must the coefficient of friction be
between your pants and that of the car seat in order that you do not slip?
11) A bicycle racer rounds a corner in a circular path with a flat surface. The combined mass of the bicycle
and rider is 80 kg. The coefficient of static friction between the bicycle tires and road is 0.60. If the
maximum speed of the racer is 8 m/s, what is the maximum radius of the curve so that he doesn’t slip and
he doesn’t have to lean into the curve?
12) You are to design a 50-m radius circular curve of highway so that cars can move along the curve and not
slip, even when the road is icy. What is the maximum speed with which the car can go if the coefficient of
friction is 0.2?
13) You (60kg) are on the Typhoon ride at Great Adventure. If the floor drops out after you are moving at 15
m/s, what must the coefficient of friction be between your back and the wall in order that you do not slip?
The radius is exactly 10-m.
14) A 210-kg go-cart travels around a level circular track whose radius is 20 m. The driver drives at constant
speed, going around 10 times in 62 seconds. If the coefficient of static friction between the tires and the
road is 0.25, what is the maximum speed at which the cart can move around the track?
15) What is the speed of a 1500-kg satellite orbiting the Earth at 7500-km above the center of the Earth?
16) What is the altitude of a 2700-kg satellite orbiting the Earth at 1200 m/s?
17) What is the minimum speed necessary for a roller coaster to make it around the top of a 12-m radius
loop?
18) What is the minimum radius loop necessary for a roller coaster to make it around the top going 20 m/s?
19) What is the minimum speed necessary for a roller coaster to make it around the top of a 15-m radius
loop?
20) What is the minimum radius loop necessary for a roller coaster to make it around the top going 15 m/s?