1. Short Version : 5. Newton's Laws Applications

2. Example 5.3. Restraining a Ski Racer
A starting gate acts horizontally to restrain a 60 kg ski racer on a frictionless 30 slope.
What horizontal force does the gate apply to the skier?
since y n
x :  
y :  x Fh Fg

3. Alternative Approach Net force along slope (x-direction) : y n   FhFg

4. 5.2. Multiple Objects  Example 5.4. Rescuing a Climber
A 70 kg climber dangles over the edge of a frictionless ice cliff.
He’s roped to a 940 kg rock 51 m from the edge.
What’s his acceleration?
How much time does he have before the rock goes over the edge?
Neglect mass of the rope. 

5.  
Tension
T = 1N throughout

6. 5.3. Circular Motion
Uniform circular motion
2nd law:
centripetal

7. Example 5.6. Engineering a Road
At what angle should a road with 200 m curve radius be banked for travel at 90 km/h (25 m/s)? y
x :
y : n   x a Fg

8. Example 5.7. Looping the Loop
Radius at top is 6.3 m.
What’s the minimum speed for a roller-coaster car to stay on track there?
Minimum speed  n = 0

9. Conceptual Example 5.1. Bad Hair Day
What’s wrong with this cartoon showing riders of a loop-the-loop roller coaster?
From Eg. 5.7: n  m g =  m a =  m v2 / r
( a  g )
Consider hair as mass point connected to head by massless string.
Then T  m g =  m a
where T is tension on string.
Thus, T = m ( g  a )  ( downward )
This means hair points upward
( opposite to that shown in cartoon).

10. Frictional Forces Pushing a trunk:
Nothing happens unless force is great enough.
Force can be reduced once trunk is going.
Static friction
s = coefficient of static friction
Kinetic friction
k = coefficient of kinetic friction
k : < 0.01 (smooth), > 1.5 (rough)
Rubber on dry concrete : k = 0.8, s = 1.0
Waxed ski on dry snow: k = 0.04
Body-joint fluid: k = 0.003

11. Example 5.11. Dragging a Trunk
Mass of trunk is m. Rope is massless. Kinetic friction coefficient is k.
What rope tension is required to move trunk at constant speed? y
y :
x : n T fs  x Fg

12. Rolling wheel:

13. Skidding wheel 滑動的輪子 :
kinetic friction 動摩擦
k  0.8
Rolling wheel 滾動的輪子 :
static friction 靜摩擦
s  1
Rolling friction 滾動摩擦
r  0.01

14. Dynamics of Wheels F fr fs

15. Example Stopping a Car
k & s of a tire on dry road are 0.61 & 0.89, respectively.
If the car is travelling at 90 km/h (25 m/s),
determine the minimum stopping distance.
the stopping distance with the wheels fully locked (car skidding).
(a)  = s : 
(b)  = k :

16. Steering Car turning to the left. Bicycle turning to the left.
More details

17. Example 5.9. Steering A level road makes a 90 turn with radius 73 m.
What’s the maximum speed for a car to negotiate this turn when the road is
(a) dry ( s = 0.88 ).
(b) covered with snow ( s = 0.21 ).
(a)
(b)

18. 5.5. Drag Forces
Drag force: frictional force on moving objects in fluid.
Depends on fluid density, object’s cross section area, & speed.
Terminal speed: max speed of free falling object in fluid.
Parachute: vT ~ 5 m/s.
Ping-pong ball: vT ~ 10 m/s.
Golf ball: vT ~ 50 m/s.
Sky-diver varies falling speed by changing his cross-section.
Drag & Projectile Motion

19. Simple Machines