# hw6a - HW#6a Page 1 of 6 Question 1, A 0.23 kg pinecone...

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Page 1 of 6 Question 1, A 0.23 kg pinecone falls 16.0 m to the ground, where it lands with a speed of 15 m/s. (a) With what speed would the pinecone have landed if there had been no air resistance? (b) Did air resistance do positive work, negative work, or zero work on the pinecone? Question 2: Work down by Normal force: W N W=N*d*cos(90) , angle between Normal force N (perpendicular to the surface) and the motion (along the surface) is 90 degrees. W N =0 Work down by gravity: W mg =mg*d*cos (90), angle between gravity (downward) and the motion (along the surface, horizontal) is 90 degrees. W mg =0. Work down by friction: W f =f k *d*cos (180), angle between friction and the motion is 180 degrees. Cos(180)=-1 , W f = - f k *d Friction is kinetic , f k = µ k *N , N=mg, W= µ k *mg*d*(-1)=0.2*9*9.81*5*(-1)= -88.2 J b). Total work is equal to change of kinetic energy: W total =W friction =K f - K i = -88.2 J So : K f =K i +W , Final Kinetic energy is equal to initial kinetic Energy plus the work down to it. The work is negative. K f is less than K i ½ mv f 2 =½ mv i 2 +W friction , Simplify it by multiply 2/m to both side of the equation, you get: v f 2 = v i 2 +W friction *(2/m) v f 2 = 7 2 +(-88.2)*(2/9) v f =5.42 m/s c). From start till become rest, W total =K rest - K initial =0 - K i = - ½ m v i 2 = - ½ *9*7 2 = -220 J This is the short way, only worries about the initial and final kinetic energy. Since f k = µ k *N is a constant force, the acceleration is constant, a=f k /m= - µ k *N/m From the acceleration and initial and final velocity, you can find out the total distance from the beginning till it stops, using our old friend, v f 2 = v i 2 +2a( x), (Note that a is negative here.) . W total =W friction = f k * x*(-1) = -220 J This is the longer way. When you know initial and final velocity, the total work equals to the change of kinetic energy is the best way for you to find total work. (no need to worry about acceleration at all). This also works for non-straight motion, for non constant acceleration, loop, complicated track, etc. It is always true that: W

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## This note was uploaded on 08/25/2010 for the course PHYS 111 taught by Professor Jamesm.lockhart during the Spring '09 term at S.F. State.

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hw6a - HW#6a Page 1 of 6 Question 1, A 0.23 kg pinecone...

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