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?sinceynx :y :xFhFg
3 Alternative Approach Net force along slope (x-direction) : y n Fh Fg
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.
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)?yx :y :nxaFg
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 awhere 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 frictions = coefficient of static frictionKinetic frictionk = coefficient of kinetic frictionk : < 0.01 (smooth), > 1.5 (rough)Rubber on dry concrete : k = 0.8, s = 1.0Waxed ski on dry snow: k = 0.04Body-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?yy :x :nTfsxFg
15 Example Stopping a Cark & 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 ForcesDrag 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