Workadditonal - WorkDonebyaConstant Force F

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Work Done by a Constant  Force  F x a b What is the work done by force  F  from  a  to  b  ? W = F (b – a) W W = F s s Graphically Work is  equal to the  area  formed by F & s
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Work Done by a Varying  Force F x F(x) a b What is the work done by force  F(x)  from  a  to   ? W =  a F(x)  dx W Graphically Work is  equal to the  area  formed by F(x) & s
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Work Done by a Varying Force :  Example F x F(x) = 5x N a = 2 m b = 6 m What is the work done by force  F(x)  from  a  to   ? W W =  a F(x)  dx W =  2 [5x 3 ] dx W = [5x 4 /4]  2   W = [5(6) 4 /4] –  [5(2) 4 /4]    W = 1,600 J
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F x a b What is the work done by force  F(x)  from  a  to   ? W = PE eb  –  PE ea W W = ½ kx 1 2  – ½  kx 2 2 k – is the spring’s force  constant Work Done by a Varying Force :               Stretching a Spring x 1 x 2 W = ½ k (x 1 2  – x 2 2 ) Graphically Work is equal to  the  area formed by F(x) & s
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 How much work is done to move the 8 kg block 10 cm to the right  if the  spring  is  initially  relaxed.  The  spring  constant  is  20  N/m,  and  the  coefficient of friction between the block and the floor were 0.5? KE 1  + PE 1  + W O  =  KE 2  + PE 2  KE 1  = ½ mv 1 = ½ (8 kg)(0)  = 0 J  PE 1G  = mgh   = (8 kg)(9.8 m/s 2 )(0 = 0 J  W O  = W f  + W F    KE 2  = ½ mv 2 = ½ (8 kg)(0)  = 0 J  PE 2G  = mgh   = (8 kg)(9.8 m/s 2 )(0) = 0 J 0  J + 0 J + 0 J + W =  0 J + 0 J + 0.1  J W =  0.1 J F net  = W net /s   =  0.1 J / 0.1 m = 1  N WORK - ENERGY (THEOREM) RELATION m m s = 10 cm = 0.1 m F  PE 2E  = ½ kx = ½ (20 N/m)(0.1 m) 2  = 0.1 J W =  W net  = 0.1 J  PE 1E  = ½ kx = ½ (20 N/m)(0) 2  = 0 J
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RECALL Contact Forces Equations for Frictional Force m w  = mg m w  = mg N N w  = mg β N θ F N = w = mg N = w y  = w cos θ N = mg cos θ N = w y   –  F y N = mgcos β sin θ   F f  f  = μN = μmg f f  f  = μN = μmg  cos θ  f  = μN f = μ(mgcos β  – F  sin θ )
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RECALL
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This note was uploaded on 05/19/2011 for the course PHYSICS 10 taught by Professor Darp during the Spring '11 term at Mapúa Institute of Technology.

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Workadditonal - WorkDonebyaConstant Force F

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