Transcript Chapter 1 Structure and Bonding

Chapter 5 Circular Motion
I.
Centripetal Acceleration
A.
Twirling a ball on a string
1) Feel tension in the string = force
2) Speed stays the same, but direction constantly changes
3) Cut the string
a) Force = 0
b) Ball would fly out maintaining its velocity
4)
B.
Since velocity is changing (direction),
we have acceleration: a = Dv/t
v1 + Dv = v2
Need a force to cause any acceleration, we feel it in the string
1) What is the direction of the force? The acceleration?
2)
Centripetal Acceleration = acceleration associated with changing
direction. It is always perpendicular to v, towards center of a curve.
C.
Size of Centripetal Acceleration
1. If speed increases, what happens to the length
of v? Dv?
2. If speed increases, change of direction happens
faster and Dv or a, gets bigger.
3.
What happens if the size of the circle decreases?
Change in direction (Dv = a) happens faster (a gets bigger).
4.
a is directly proportional to v2 and inversely proportional to r
2
2
1
ac 
D.
r
ac  v
v
ac 
r
Force and centripetal acceleration
1. F = ma, we know we must have a force to get an acceleration
2. Tension = force for a ball on a string
a) Tv = W
b) Th = force causing cent. accel.
3. 0.05 kg ball, r = 0.4 m, v = 2.5 m/s a?, Tv? Th?
II.
Centripetal Force
A.
Centripetal Force = one force or a sum of forces causing a
centripetal acceleration
1. Analyze each situation to find sum of forces
2. Possible contributors = friction, gravity, normal, etc…
B.
How does a car turn a corner?
1. No string, no tension to cause the centripetal acceleration
2.
Friction provides the centripetal force
a) Static Friction: no motion between surfaces in direction of the force = fs
b) Kinetic Friction: motion between surfaces in direction of the force = fk
c) For same 2 surfaces, fS > fK
3.
4.
When the car is not skidding: fS,
F = mac
v2 
FS  m 
 r 
v2
ac 
r
a)
b)
5.
C.
Velocity is squared so it has a large effect on force: 2 x v = 4 x F
Radius and mass just have “normal” effects on force
When the car is skidding it has a much smaller force fK
a) The force may not be enough to hold the car, like a broken string
with the ball
b) fS and fK are very small for ice/tire interactions, skid easily
Turning on a banked curve
1. Nv = W
2. Nh = centripetal force, is proportional to W
a) Angle (q), W affect Nh, the size of the force
Nh
q
Nh
q
b)
c)
d)
D.
N,F
W
2


v
Speed also affects the size of the force needed
F  m 
 r 
Mass of the car doesn’t matter
 v2 
FC  m   W  mg
 r 
Total Centripetal Force can be larger than Nh because of friction
Fc = Nh + fS
Can have a range of speeds that require some or no friction to help.
Ferris Wheel
1. Bottom: N > W, feel heavy
N – W = centripetal force
N
2.
Sides: N = W, f is centripetal force
3.
Top: N < W, feel light or even weightless
W – N = centripetal force
4.
What happens if you go faster?
F
N W
W,F