Inclined Planes. Physics is infamous for sliding blocks down inclined planes. How boring! Why do we study it?

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1 Inclined Planes Physics is infamous for sliding blocks down inclined planes How boring! Why do we study it? Many things we do involve inclines. Boxes are an easy way to simplify many complex objects.

2 My Icy Driveway When my driveway is a sheet of ice (ignore friction), how fast do I need to be driving to get to the top of my driveway? Garage ~15 Road 3 m (~10 feet) Inclined Driveway

3 Making 2 dimensions only 1! y Better, unless need to determine centripetal force (Ch.7) x A B Why would I change x and y? In Case A, need a x, a y, v x, v y, x, y? Have to break up the vector components In Case B: y=0, v y =0 Acceleration changes though: a x =±9.8 sinθ

4 Why a x =±9.8 Sinθ? anics/forces/inclinedplane/inclinedplane.html (Based on similar triangles argument) y y component of acceleration Draw a line parallel to y axis from start of vector Draw a line parallel to x axis from end of vector θ g x component of acceleration x θ SAME ANGLE! Does the acceleration in the y direction mean that it will change velocity in y direction? (Tricky question)

5 My Icy Driveway When my driveway is a sheet of ice (ignore friction on slope), how fast do I need to be driving to get to the top of my driveway? Is this feasible on an icy day? ~20 feet ~15 Road ~10 feet Garage Inclined Driveway Acceleration of starting for a typical car is only 0.5g. So, how could I get out of my driveway?

6 watch?v=rzehncbu1_g Introduction to Friction YouTube is a wonderful resource for physics videos (in addition to other fun stuff)

7 Main Ideas in Class Today Kinetic Friction Static Friction Friction w/inclines Solving Problems Extra Practice: 4.39, 4.41, 4.61, 4.63

8 Friction Kinetic friction: force that opposes the motion of an object when sliding against a surface (even air causes air resistance) Friction is the reason you always have to put energy into machines in order for them to continue working. The amount of friction between two objects depends upon how smooth or rough the surfaces are. No surface is perfectly smooth.

9 Kinetic Friction (f k ): friction when moving, slows you down f k = µ k n (Greek letter µ pronounced mu ) f k µ k is coefficient of kinetic friction, depends on surface (table 4-2 in book gives examples) equation valid for magnitudes only ( vector formula) since f k n n F pull Draw a free body diagram mg If you are pulling this, do you want much friction?

10 Pushing or Pulling: Does it make a difference to the amount of friction? n F push F pull f k f k = µ k n F push n mg F pull Remember: There is not only one formula for normal force! f k mg Pushing down on the box will increase the normal force and thus friction!

11 Stopping distance What is the acceleration of the object? If it starts at a velocity of 10 m/s, how far will it go before it stops? n f k coefficient of kinetic friction is 0.4 mg +x

12 Static Friction Force that keeps object from sliding against a surface when it is at rest F stat µ s n µ s is coefficient of static friction, also depends on surface equation valid for magnitudes only ( vector formula) Static friction force increases with applied force until object starts moving: F stat,max = µ s n F fr =µ s n Once it starts moving, kinetic friction takes over. Kinetic friction is less than the maximum static friction.

13 Hockey puck A hockey puck is struck by a hockey stick and given an initial speed of 20.0 m/s on a frozen pond. The puck remains on the ice and slides 120 m, slowing down steadily (AKA constant acceleration) until it comes to rest. Determine the coefficient of kinetic friction between the puck and the ice. n

14 A 20 kg sled slides down a hill after receiving a tiny shove (only enough to overcome static friction, not enough to give significant initial velocity). A) If there is friction of µ k =0.1, what is the acceleration of the sled? B) If the length of the hill is 20 m, how long does it take the sled to reach the bottom of the hill if it starts from rest? Inclines & Friction 20 m 30 o

15 A cable attached to a car pulls the car up the ramp (angle α). Which direction should friction point? A. B. C. D. Inclines & Friction E. not enough information given to decide Q44

16 A cable attached to a car lowers the car down the ramp (angle α). Which direction should friction point? A. B. C. D. E. not enough information given to decide Q45

17 If the cable moves at a constant speed, in which case (if any) would the tension in the chain be larger? A. When car goes up ramp B. When car goes down ramp C. Both cases would have the same tension D. Not enough information given to determine Q46

18 A. B. C. D. Q47

19 A. B. C. D. E. Q48

20 Rolling Along or Not (A little tricky, but useful to know) What kind of friction allows you to roll things? For example, your car tires on the road. A)Static friction B)Kinetic friction C)Both D)Neither Q49

21 This person weighs 170 lb. Each crutch makes an angle of θ = 22.0 with the vertical (as seen from the front). Half of the person's weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet. Assuming he is at rest and the force exerted by the ground on the crutches acts along the crutches, determine the smallest possible coefficient of friction between crutches and ground.

22 Clicker Answers Chapter/Section: Clicker #=Answer Ch.2A: 1=D, 2=E, 3=D, Ch.2B: 4=B, 5=C, 6=A, 7=C, 8=E Ch.2C: 9=A, 10=C, 11=B, 12=C, 13=E, 14=A Ch.3A:15=B, 16=C, 17=B, 18=D, 19=A Ch.3B: 20=C, 21=B, 22=B (hard), 23=A Ch.4A: 25=A, 26=B, 27=E, 28=C, 29=C, 30=D, 31=C, 32=D, 33=C, 34=B, 35=D Ch.4B: 36=A, 37=C, 38=B, 39=E, 40=B, 41=B, 42=C, 43=A Ch.4C: 44=B, 45=A, 46=A, 47=C, 48=C, 49=A