33_horiz_vert - Lesson 33 Horizontal Vertical Circular...

Lesson 33: Horizontal & Vertical Circular Problems
There are a wide variety of questions that you do if you apply your knowledge of circular motion
correctly.
●
The tough part is figuring out how to set them up.
●
You need to figure out two things at the start
1. Is the circle the object is moving in horizontal or vertical?
2. What combination of forces are causing the centripetal force?
Horizontal Circle Problems
A horizontal circle is any circle that lies flat parallel to the ground.
●
A perfect example is a car going around a regular traffic circle.
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This path can be a complete circle or even just a portion of a circle (as long as you can still
measure basics like what the radius would have been if it had been a complete circle).
●
If the object is on the ground, it is very common to say that the needed centripetal force is
caused by the force of friction with the ground.
Example 1 : A construction team is looking at building a turn on a highway road. They are concerned
that cars should be able to go through the turn without skidding off the road even in conditions are bad.
Determine the minimum radius that can be used for the curve of the turn if a car traveling 110 km/h
might be traveling in conditions that cause a coefficient of static friction of only 0.60 between the tires
and the road.
●
Since the car is moving in a circle there is a centripetal force, caused by the friction between the
tires and ground. As the tires push outwards on the ground, the ground pushes inwards on the
tires.
●
You can see the force of the tires pushing the ground outwards in situations when a car is going
around a turn on a gravel road; you can see the gravel being shot outwards from the circle.
F
c
= F
f
mv
2
r
= F
N
mv
2
r
= F
g
mv
2
r
= mg
v
2
r
= g
r =
v
2
 g
r =
30.6
2
0.60  9.81 
r = 1.6e2 m
12/2/2007 © studyphysics.ca Page 1 of 4 / Section 5.2
We start by substituting formulas for each side of the relationship.