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Work = Force X distance W = Fd W = Fdcos q Unit – Joules Force must be direction of motion

Work = Force X distance W = Fd W = Fdcos q Unit – Joules Force must be direction of motion W NET = D KE. Work or Not. A teacher pushes against a wall until he is exhausted. A book falls off the table and falls freely to the ground.

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Work = Force X distance W = Fd W = Fdcos q Unit – Joules Force must be direction of motion

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  1. Work = Force X distance W = Fd W = Fdcosq • Unit – Joules • Force must be direction of motion WNET = DKE

  2. Work or Not • A teacher pushes against a wall until he is exhausted. • A book falls off the table and falls freely to the ground. • A waiter carried a full try of meals across the room. • A rocket accelerates through space.

  3. Mr. Fredericks pulls a 10 kg box with 30 N of Force a distance of 50 m, at an angle of 50o with the ground. • Calculate the work that was done (964 J) • Calculate the normal force on the suitcase. (75 N) Direction of motion q = 50o

  4. Work: Example 4 A 50-kg crate is pulled 40 m with a force of 100 N at an angle of 37o. The floor is rough and exerts a frictional force of 50 N. Determine the work done on the crate by each force and the net work done on the crate. Fp q Ffr FN mg

  5. A 150,000 kg rocket launches straight up with a thrust of 4.0 X 106 N. • Calculate the work done by thrust at 500 m. (2.0 X 109 J) • Calculate the work done by gravity. (-7.4 X 108 J) • Calculate the net work. (1.26 X 109 J) • Calculate the speed of the rocket. (130 m/s)

  6. A 500 g air hockey puck slides across an air table at 2.0 m/s. The player blows on the puck at an angle of 30o to the horizontal with a force of 1.0 N for 50 cm. The player is trying to slow the puck. • Calculate the work done by the player. (-0.433 J) • Calculate the final speed of the puck (1.5 m/s)

  7. Work: Variable Force Work is really an area: W =∫Fdx (an integral tells you the area) WORK

  8. The magnitude of a force on a spring varies according to F(x) = 1500x2. Calculate the work done stretching the spring 10 cm from its equilibrium length. W =∫00.10mFdx W =∫00.10m1500x2dx W = 500x3| 00.10m = 0.50 Joules

  9. A 1500 kg car accelerates from rest. The graph below shows the force on the car. • Calculate the work done on the car. (1 X 106 J) • Calculate the speed after 200 m. (37 m/s)

  10. A 100 g pinball is launched by pulling back a 20 N/m spring a distance of 20 cm. However, there is friction and mk = 0.10. • Calculate the work done by the spring. (0.400 J) • Calculate the work done by friction. (-0.020 J) • Calculate the speed of the ball on release. (2.8 m/s)

  11. Does the Earth Do Work on the Moon? W = Fdcosq W = Fd(cos 90o) W = Fd(0) W = 0 v FR

  12. English Unit of Work • Foot-pound – English unit of work. • Pound – unit of Force • Foot – Unit of distance • W = Fd = (foot*pound)

  13. A 70 kg is gliding at 2.0 m/s when he starts down a slippery 10o slope. He travels for 50 m. • Calculate the force parallel to the ground pulling him down the hill. • Calculate work done by gravity for the 50 m. • Calculate his speed at the bottom. Remember that initially he was not at rest.

  14. Conservative and Nonconservative Forces Conservative Forces • Work is independent of the path taken • Gravity, electromagnetic forces Nonconservative Forces • Work depends on the path taken • Friction (dissipative forces)

  15. Nonconservative Forces Will it take more work to push the box on path A or path B? Or are they the same? B A

  16. If nonconservative forces act, use: KE1 + PE1 = KE2 + PE1 + Wfr ½ mv2 + mgy = ½ mv2 + mgy+ Ffrd

  17. Mr. Fredericks (100 kg) slides down a 3.5 m tall slide. If he leaves the slide at the bottom at 6.3 m/s, what is the Force of friction and the coefficient of friction for the slide? Assume the slide is 6.0 m long. (0.25) 3.5 m 6.0 m

  18. A 70 kg skier starts at the top of the slope at 2.0 m/s. The slope is 50 m long and has an elevation of 10o. There is a wind exerting a 50 N retarding force at the bottom. • Calculate the work done by gravity • Calculate the work done by the retarding force • Calculate his speed at the bottom (10 m/s)

  19. A 5.0 kg box is attached to one end of a spring (80 N/m). The other end is attached to the wall. The spring is stretched 50 cm by a constant force of 100 N. There is friction and mk = 0.30. • Calculate the work done by the pull • Calculate the work done on the spring • Calculate the work lost to friction (thermal energy) • Calculate the speed of the box at 50 cm (3.6 m/s)

  20. Force and Potential Energy F = - dU ds • Force is the negative of the derivative of the potential energy. • Force is the negative slope.

  21. Example: Calculate the gravitational force for gravitational Potential energy (mgy)

  22. Calculate the force being exerted on a particle given the following potential energy curve:

  23. Given the following potential energy graph, sketch the force versus distance graph.

  24. Power Power = Work P = W time t • Metric Unit: Joules/s = Watt. • Definition – rate at which work is done • A powerful engine can do a lot of work quickly. • Running and walking up the steps require the same amount of work. • Running up steps requires more Power

  25. A donkey performs 15,000 J of work pulling a wagon for 20 s. What is the donkey’s power? • What power motor is needed to lift a 2000 kg elevator at a constant 3.0 m/s? (Hint: use 1 second in your calculations) • A motor and cable drags a 300 kg box across a rough floor at 0.50 m/s. The coefficient of kinetic friction is 0.60. Calculate the necessary power.

  26. Horsepower • The English Unit of power is horsepower • Foot-lb = Horsepower (hp) second • 1 hp = 746 Watts • 1 hp = ½ Columbus (who sailed in 1492)

  27. How much horsepower is required to power a 100 Watt lightbulb? • A 1500 kg car has a profile that is 1.6 m wide and 1.4 m high. The coefficient of rolling friction is 0.02. • Calculate the drag force if the car travels at a steady 30 m/s (1/4Av2) (504 N) • Calculate the force the car must exert against drag and friction. (798 N) • Calculate the power the engine must provide if 25% of the power is lost between the engine and the wheels.

  28. Horsepower Consider a 40 hp car engine that can go from 0 to 60 mi/hr in 20 seconds. A 160 hp car could go from zero to 60 mi/hr in 5 seconds. 4 times as powerful means it can do the same work in ¼ the time.

  29. Horsepower: Example 4 A crane lifts a 200 N box 5 meters in 3 seconds. What is the crane’s power in Watts and in horsepower?

  30. Power and Calculus P = W t Work = Fd P = Fd t P = Fv

  31. Power and Calculus: Ex 1 Find the power delivered by a net force at t=2 s to a 0.5 kg mass that moves according to x(t) = 1/3t3 v = dx/dt v = t2 v = (2)2 = 4 m/s a = dv/dt a = 2t a = 4 m/s2

  32. F = ma F = (0.5 kg)(4 m/s2) = 2 N P = Fv = (2N)(4 m/s)

  33. Springs and Calculus The force in a spring is variable (F = -kx) Work =∫0x F(x) dx Work = ∫0x -kx dx Work = - ½kx2 Work = -DPE DPE = ½ kx2

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