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A child of mass m rides on a sled down a slick, ice-covered hill inclined at an angle θ with respect to the horizontal. a)What is the acceleration of the child b)What is the normal force exerted on the child by the sled Quiz 1. Draw a sketch 2. Draw a free body diagram 3. Set Cartesian coordinates (make a smart choice) 4. Find all x and y components of all forces and the acceleration 5. Write down Newton’s Second Law for the components Hint: Remember, that normal force is always perpendicular to a surface A child of mass m rides on a sled down a slick, ice-covered hill inclined at an angle θ with respect to the horizontal. a)What is the acceleration of the child b)What is the normal force exerted on the child by the sled Quiz N a θ W ΣF=Fnet x y N 0 N W -mgsin θ -mgcosθ ma -ma 0 mg sin θ = ma a = g sin θ N – mg cos θ = 0 N = mg cos θ Place a block on a table. Attach a large spring scale to the block. Pull the scale harder and harder. The scale reading increases more and more, then the scale pulls hard enough, and the block starts moving. Place a block on a table. Attach a large spring scale to the block. Pull the scale harder and harder. The scale reading increases more and more, then the scale pulls hard enough, and the block starts moving. The scale pulls on the block, which does not start moving The scale pulls harder, but the block still does not start moving N Ffr W N N Pull Ffr Pull W The block is on the table, at the moment just before it starts moving Ffr W The scale pulls the block with constant velocity N N Pull Ffr W The scale pulls harder, so the block moves with an acceleration Pull Ffr W Pull Friction Friction Fk k N Fsmax Fk N Fk Fs max s N 0 Static Kinetic Pull A child of mass m rides on a sled down a rough hill inclined at an angle θ with respect to the horizontal. The coefficient of the kinetic friction is μk and static friction is μs a)What is the acceleration of the child b)What is the normal force exerted on the child by the sled x y N 0 N W -mgsin θ -mgcosθ Ffr Ffr=μkN 0 ma -ma 0 N Ffr a θ W μkN - mg sin θ = -ma a N – mg cos θ = 0 a = μkN/m - g sin θ N = mg cos θ a = μkg cos θ - g sin θ N = mg cos θ A block of mass m is placed on a board that could be inclined with respect to the horizontal. The coefficient of the kinetic friction is μk and static friction is μs. a=0 At what angle θ the board starts sliding? x y N 0 N W -mgsin θ -mgcosθ Ffr Ffr=μsN 0 ma -ma 0 N Ffr a θ W a = μsg cos θ - g sin θ 0 = μsg cos θ - g sin θ N = mg cos θ tan θ = μs Homework (due Monday) Section 4.5, 4.6 (Examples!!!!) Problems (p.111) #20, 32, 35, 36, 40, 45 Friction 0 Quiz Fk N Fsmax Fk Static Kinetic Fk k N Fs max s N Pull A block of mass m is projected with an initial speed v0 along the horizontal plane with coefficient of kinetic friction μk and of static friction μs. How far will the block go until it stops?