2 Why doesn’t the roller coaster fall its loop-the loop track? Ans. The downward net force is just enough to make it move in a circular path.
3 5.1. Using Newton’s 2nd Law Example 5.1. Skiing A skier of mass m = 65 kg glides down a frictionless slope of angle = 32. FindThe skier’s accelerationThe force the snow exerts on him.yx :nay :xFg
4 Example 5.2. Bear Precautions Mass of pack in figure is 17 kg.What is the tension on each rope?sincex :yy :T2T1xFg
5 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
6 Alternative Approach Net force along slope (x-direction) : y n Fh Fg
7 GOT IT? 5.1. A roofer’s toolbox rests on a frictionless 45 ° roof, secured by a horizontal rope.Is the rope tensiongreater than,less than, orequal tothe box’s weight?nx :TSmaller smaller TFgx
8 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.
12 Example 5.5. Whirling a Ball on a String Mass of ball is m. String is massless.Find the ball’s speed & the string tension.x :y :yTaxFg
13 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
14 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
15 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 / rConsider hair as mass point connected to head by massless string.Then T + m g = m awhere T is tension on string.Thus, T = n.Since n is downward, so is T.This means hair points upward( opposite to that shown in cartoon ).
16 5.4. Friction The Nature of Friction Some 20% of fuel is used to overcome friction inside an engine.The Nature of Friction
17 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
18 Application of Friction Walking & driving require static friction.No slippage:Contact point is momentarily at rest static friction at workfoot pushes groundground pushes you
19 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 :
21 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)
22 Example 5.10. Avalanche! Storm dumps new snow on ski slope. s between new & old snow is 0.46.What’s the maximum slope angle to which the new snow can adhere?ynx :y :fsxFg
23 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
24 GOT IT? 5.4 Reason: Chain is pulling downward, thus increasing n. Is the frictional forceless than, (b) equal to , or (c) greater thanthe weight multiplied by the coefficient of friction?Reason: Chain is pulling downward, thus increasing n.
25 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