1. A vs m, a vs 1/m, F vs m, F vs a F = ma F = am a = F(1/m ) F = ma F m

2. A vs m, a vs 1/m, F vs m, F vs a F = ma F = am a = F(1/m ) F = ma F m

3. Transportation: Ch. 1, Act. 7
Driving on Curves
Transportation: Ch. 1, Act. 7

4. Motion & Forces
Velocity – a measure of the change in distance over time with direction (v = Δd/Δt).
Mass – A measure of the amount of matter an object contains (m).
Acceleration – A measure of the change in velocity over change in time (a = Δv/Δt).
Force – A push or pull that is equal to the mass of the object multiplied by its acceleration (Fc = mac).

5. Uniform Circular Motion
If an object is moving at constant speed in a circular path, can it be accelerating?
YES!
Although the speed may be constant, the direction is changing.
If direction is changing over time, then the velocity must be changing.
Acceleration, by definition, is the change in velocity over time (a = v/t).
If the velocity is changing over time, then the object must be accelerating.

6. Newton’s 1st Law
In order to make an object move in a circular path, an outside force must be must exist.
Newton’s 1st Law says that an object will attempt to remain in motion in a straight line at a constant speed unless an unbalance force acts on it.
To make an object move in a circular path, centripetal force must be applied to the object.
Centripetal force always acts toward the center of the circle that the object moves.

7. Circular Motion – Centripetal Force
Centripetal force acts perpendicular or at right angles to its direction of motion.
Instantaneous direction of velocity
Direction of force required to make object move in a circular path (towards the center)

8. Centripetal Force Centripetal force is affected by:
The mass of the object (m).
The speed of the object around the circle (v).
The radius of the circle (r).
Using Newton’s 2nd Law of Motion (F = ma), centripetal force is mathematically represented as follows:
Where: ac = v2/r

9. What do you think?
You are driving along a road at the posted speed limit of 40 mph (20 m/s). A road sign warns you that you are approaching a curve and tells you to slow down to 20 mph (10 m/s).
Why are they telling you to slow down?
If your speed is too fast, you may lose grip with the road while going around the turn.
Factors such as rain and snow need to be considered while negotiating turns.

10. What Factors Affect Centripetal Force and How?
Centripetal force will increase as:
the mass of the object increases.
The speed of the object increases.
The radius of the circle decreases.
Mass
Force
Speed
Force
Radius
Force

11. The object would go straight due to inertia
The path of objects.
If the centripetal force were suddenly removed from an object moving in a circular path, what trajectory (or path) would it follow? Why?
The object would go straight due to inertia

12. Determining the Speed
How would you determine the speed of an object moving in a circular path?
What you already know:
v = Δd/Δt
Circumference of a circle: C = 2πr
If you know the time (T) it takes an object to make one full revolution and the radius of the circle it traverses, then the objects speed can be determined as follows:
v = C/T
v = 2πr/T

13. Example 1
A person at the equator travels once around the circumference of the Earth in 24 hours. The radius of the Earth is 6,400 km. How fast is the person going?
v = d/t
d = 2πr = 2•π•6,400 km = 40,192 km
t = 24 hours = 24 • 60 min/hr • 60 sec/min = 86,400 s
v = km/86,400 s = 465 m/s (~1,000 mph)

14. Example 2
Earth travels in a circular path around the sun. The radius of the orbit of the Earth’s path around the sun is about 1.5 x 108 km. What is the speed of the Earth in its orbit?
d = 2πr = 2•π•1.5 x 108 km = 9.42 x 1011 km
t = 365 days x 24 hr/day = 8,760 hr
v = d/t = 9.42 x 1011 m/8,760 x 103 hr
v = 107,589 km/hr (~66,705 mph)

15. Example 3
Friction can hold a car on the road when it is traveling at 20 m/s and the radius of the turn is 15 m. What happens if:
The turn is tighter?
The force due to friction will need to increase.
The speed is increased?
The car will likely go off the road is a straight path.
The road is more slippery.
The car will likely go off the road in a straight path.

16. Objects that travel in circular paths. What is the cause of the force?
The Earth – Sun System:
Gravity.
A racecar traveling around a turn on the racetrack:
Friction.
An athlete throwing the hammer:
Tension in the cable attached to the hammer.

17. Key Ideas Roller Coaster: In going around in a circle
ac > g or you will die. (ac = v2/r)
In going around in a circle
As you go faster you need more force to hold you in place
Friction.
As you go tighter in a circle at the same speed, you need more force to hold you in place

18. Just For Fun