5.3 – Horizontal and Vertical Motion
1. Determine the maximum speed at which a 2000.0-kg car can round a curve that has the radius of
60.0 m, if the coefficient of friction between the tires and the road is 0.30. [ 13m/s ]
2. A 1600 kg truck travels around a curved section of level roadway having a radius of 60 m.
Determine the maximum possible speed that would allow the truck to stay on the road if it is on:
a) Dry pavement with a coefficient of friction 0.60 [19 m/s]
b) Slippery pavement with a coefficient of friction of 0.20 [11 m/s]
3. At a yo-yo competition, a blue 200 g yo-yo is spun about a competitor’s head at a constant speed,
with a diameter of rotation of 1.20 m. If the yo-yo makes one complete horizontal revolution
each second, determine the tension in the string. [4.73 N]
4. A Spruce Grove PAC Saint (m= 90.0 kg) carves a turn with a radius of 3.40 m while skating and
feels his skates begin to slip on the ice. What is his speed if the coefficient of static friction
between the skates and the ice is 0.80? [5.2 m/s]
5. A 600.0-g toy radio-controlled car can make a turn at a speed of 3.0 m/s on the kitchen floor
where the coefficient of static friction is 0.90. What is the radius of its turn? [1.0 m]
6. A 900.0-kg roller coaster car full of people goes around a vertical loop that has a diameter of
100.0 m. What minimum speed must the roller coaster car have at the top of the vertical loop to
stay on the track? [22.1 m/s]
7. Assuming the force due to gravity is 10.0 N and the centripetal force is 16.0 N, determine the
tension at :
i)
The top of the circle [6.0 N]
ii)
The bottom of the circle [26.0 N]
8. An 800 g rock is tied to a string and whirled in a vertical circle with a 75 cm radius and a
frequency of rotation of 1.6 Hz. Assuming a constant velocity, determine the tension in the rope
at:
a) Top of the circle [53 N]
b) Bottom of the circle [68 N]
9. The minimum possible velocity for a mass on a string in vertical circular motion to maintain a
constant radius occurs when the tension in the string is equal to zero at the top of the circle.
Determine the minimum possible velocity for a 500 g rock on the end of an 80 cm long string
showing vertical circular motion. [2.8 m/s]
10. Neglecting friction, what is the minimum speed a toy car must have to go around a vertical loop
of diameter 15.0 cm without falling off? [1.21 m/s]
11. What is the maximum radius a roller coaster loop can be if a car with a speed of 20.0 m/s is to go
around safely? [40.8 m]
12. A bucket filled with sand swings in a vertical circle at the end of a rope with increasing speed. At
some moment, the tension on the rope will exceed the rope’s strength, and the rope will break. In
what position in the bucket’s circular path is this most likely to happen? Explain.
13. Is it necessary to know the position of an object moving in a vertical circle with uniform speed if
you are determining centripetal force? Explain.
14. A 1300 kg car is travelling at 25 m/s as it drives through a dip between two hills
that have a radius of curvature of 120 m. Determine the normal force acting on
the car at the bottom of the dip. [20 kN]
15. A 1300 kg car is travelling at 25 m/s as it drives through the crest between two
hills that have a radius of curvature of 120 m. Determine the normal force
acting on the car at the crest of the dip. [6.0 kN]
16. A 400 kg roller coaster car passes upside down at the top of a loop-de-loop having a radius of 30
m. The centripetal force at the top is the result of two sources: the normal force of the track
pushing down on the car and with the force due to gravity acting on the car. Determine the
magnitude of the normal force if the centripetal force is 5000 N at the top of the loop. [1.1 kN]
17. When airplane pilots execute turns at high speeds they may feel heavier or lighter than their
normal weight. The normal weight is called 1 G. Double the normal weight is 2Gs. The
Canadian Forces Snowbird aerobatics team flies nine Canadian CT-114 Tutor airplanes for air
shows. Assuming a vertical loop-de-loop with a radius of 778 m is performed by a 75.0 kg pilot;
determine the speed of the airplane at:
a) top of the loop-de-loop if the pilot experiences 0.510 G forces? [107 m/s]
b) bottom of the loop-de-loop if the pilot experiences 3.78 G forces [146 m/s]