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Physics 1710 Chapter 7—Work

r. v. 0. Physics 1710 Chapter 7—Work. Answer: a = v 2 /r = (15 m/s) 2 /(0.2 m) =1125 m/s 2 a~113 g!!! F = m a = (1.00 x 10 – 4 kg )/(1.1 x10 3 m/s 2 ) = 0.11 kg m/s 2 = 0.11 N. Which way will the ant fly off?. m. 0. Physics 1710 Chapter 7—Work. Query:

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Physics 1710 Chapter 7—Work

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  1. r v 0 Physics 1710 Chapter 7—Work Answer: a = v 2 /r = (15 m/s)2/(0.2 m) =1125 m/s2 a~113 g!!! F = m a = (1.00 x 10 – 4kg)/(1.1 x10 3 m/s2) = 0.11 kg m/s2= 0.11 N Which way will the ant fly off? m

  2. 0 Physics 1710 Chapter 7—Work Query: What was the most significant international development to occur in the 19th century?

  3. No Talking! Think! Confer! 0 Physics 1710 Chapter 7—Work Most significant international development of in the 19th century (1800 s)? Peer Instruction Time

  4. 0 Physics 1710 Chapter 7—Work Our concept of work changed forever. What was the “Industrial Revolution?”

  5. 0 Physics 1710 Chapter 7—Work 1′ Lecture Work is defined to be the distance traveled multiplied by the distance over which the force acts. ΔW = ∫abF•d r

  6. 0 Physics 1710 Chapter 7—Work Work: Work is the product of the distance moved in the direction of the force and the magnitude of the force. OR Work is the distance moved multiplied by the component of the force in the direction moved.

  7. 0 Physics 1710 Chapter 7—Work Work: dW = F•d r = “Force times distance” Note • = “Scalar Product,” “inner product,” “dot product” dW = F•d r = Fx dx + Fy dy + Fz dz OR dW = F•d r =F cos dr

  8. B By A Ay Bx Ax 0 Physics 1710 Chapter 7—Work Scalar Product: A•B ≡ Ax Bx+ AyBy + Az Bz

  9. B By A Ay Bx Ax 0 Physics 1710 Chapter 7—Work A•B= AB cos θ Scalar Product: A•B ≡ Ax Bx+ AyBy + Az Bz θ β α ABcos θ = ABcos(β-α) = AB[cos(β)cos(α) +sin(β)sin(α)] = Acos(α)Bcos(β) + Asin(α)Bsin(β) = Ax Bx+AyBy

  10. 0 Physics 1710 Chapter 7—Work Scalar Product: (properties) A•A = Ax2 + Ay2 + Az2 = ⃒A⃒2 A•B = B•A A•(B + C) = A•B + A•C

  11. 0 Physics 1710 Chapter 7—Work Work: W = ∫F•d r “Scalar Product” W = ∫F•d r = ∫ Fx dx + ∫ Fy dy + ∫ Fz dz OR W = ∫ F•d r =∫F cos dr

  12. 0 Physics 1710 Chapter 7—Work Unit of Work: [F ‧ d ] = N‧m = Joule = J Joule

  13. 0 Physics 1710 Chapter 7—Work Scalar Product: A•B = a scalar A•B = Ax Bx + Ay By + Az Bz A•B = AB cos  Unit vectors: i‧i = j‧j = k‧k = 1 Orthogonal: i‧j = i‧k = j‧k = 0

  14. 0 Physics 1710 Chapter 7—Work Work done by varying Force: W = ∫ F•dr For Example: Spring Fspring = - k x W = ∫ Fspring d x = ∫ -x 0(-k x) dx = ½ k x 2

  15. 0 Physics 1710 Chapter 7—Work Work Done : W = ∫ F ‧d x = ∫[0.5 x3 ]dx = ¼ (0.5) x 4=1 ¼ (0.5) (0.2) 4 = 0.2 mJ

  16. 0 Physics 1710 Chapter 7—Work Work Done to accelerate body: The work done to accelerate a body from a speed vi to a speed vf is F = ma W = ∫ ma ‧d x = m∫[dv/dt ]vdt = m∫ifvdv = ½ m vf 2 - ½ m vi 2

  17. 0 Physics 1710 Chapter 7—Work Summary Work is defined to be the distance traveled multiplied by the distance over which the force acts. W = ∫ F•d r [Joules] = [N ][m]

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