# Work or Not. Work: Example 4. Lab Comments 6/3/2013. Work = Force X distance W = Fd W = Fdcosq

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1 Work = Force X distance W = Fd W = Fdcosq Unit Joules Force must be direction of motion W NET = DKE Work or Not 1. A teacher pushes against a wall until he is exhausted. 2. A book falls off the table and falls freely to the ground. 3. A waiter carried a full try of meals across the room. 4. A rocket accelerates through space. Mr. Fredericks pulls a 10 kg box with 30 N of Force a distance of 50 m, at an angle of 50 o with the ground. a. Calculate the work that was done (964 J) b. Calculate the normal force on the suitcase. (75 N) Direction of motion Work: Example 4 A 50-kg crate is pulled 40 m with a force of 100 N at an angle of 37 o. 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. (1200 J) F p q = 50 o F fr F N mg q Lab Comments First sentence should be summary/purpose Free body Force was constant in graph A 150,000 kg rocket launches straight up with a thrust of 4.0 X 10 6 N. a. Calculate the work done by thrust at 500 m. (2.0 X 10 9 J) b. Calculate the work done by gravity. (-7.4 X 10 8 J) c. Calculate the net work. (1.26 X 109 J) d. Calculate the speed of the rocket. (130 m/s) 1

2 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 30 o to the horizontal with a force of 1.0 N for 50 cm. The player is trying to slow the puck. a. Calculate the work done by the player. ( J) b. Calculate the final speed of the puck (1.5 m/s) Work: Variable Force Work is really an area: W = Fdx (an integral tells you the area) WORK The magnitude of a force on a spring varies according to F(x) = 1500x 2. Calculate the work done stretching the spring 10 cm from its equilibrium length. A 1500 kg car accelerates from rest. The graph below shows the force on the car. a. Calculate the work done on the car. (1 X 106 J) b. Calculate the speed after 200 m. (37 m/s) (0.50 Joules) A 100 g pinball is launched by pulling back a 20 N/m spring a distance of 20 cm. However, there is friction and m k = a. Calculate the work done by the spring. (0.400 J) b. Calculate the work done by friction. ( J) c. Calculate the speed of the ball on release. (2.8 m/s) Does the Earth Do Work on the Moon? W = Fdcosq W = Fd(cos 90 o ) W = Fd(0) W = 0 v F R 2

3 English Unit of Work Foot-pound English unit of work. Pound Force Foot distance W = Fd = (foot*pound) A 70 kg man on a sled is gliding at 2.0 m/s when he starts down a slippery 10 o slope. He travels for 50 m. a. Calculate the force parallel to the ground pulling him down the hill. (120 N) b. Calculate work done by gravity for the 50 m. (6000 J) c. Calculate his speed at the bottom. Remember that initially he was not at rest. (13 m/s) 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) Nonconservative Forces Will it take more work to push the box on path A or path B? Or are they the same? B A If nonconservative forces act, use: KE 1 + PE 1 = KE 2 + PE 1 + W fr ½ mv 2 + mgy = ½ mv 2 + mgy + F fr d 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. (0.31) 3.5 m 6.0 m 3

4 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 10 o. There is a wind exerting a 50 N retarding force at the bottom. a. Calculate the work done by gravity (6000 J) b. Calculate the work done by the retarding force. (-2500 J) c. Calculate her speed at the bottom (10 m/s) 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 m k = a. Calculate the work done by the pull. (50 J) b. Calculate the work done on the spring. (10 J) c. Calculate the work lost to friction (thermal energy). (7.4 J) d. Calculate the speed of the box at 50 cm (3.6 m/s) [W = 1 / 2 mv / 2 kx 2 + E therm ] Force and Potential Energy F = - du ds Force is the negative of the derivative of the potential energy. Force is the negative slope. Example: Calculate the gravitational force for gravitational Potential energy (mgy) Calculate the force being exerted on a particle given the following potential energy curve: Given the following potential energy graph, sketch the force versus distance graph. 4

5 A gram box is pushed up a 30 o incline with a force of 50.0 N as shown in the figure. The box moves 50.0 cm up the incline. Calculate the work done by the force assuming no friction. Calculate the work done against gravity and the net work done by all the forces on the box. Suppose the box has a mass of 500 grams and m k = Calculate the net work done by all the forces on the box. Power = Work time Power P = W 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 a. A donkey performs 15,000 J of work pulling a wagon for 20 s. What is the donkey s power? b. 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) c. A motor and cable drags a 300 kg box across a rough floor at 0.50 m/s. The coefficient of kinetic friction is Calculate the necessary power. Horsepower The English Unit of power is horsepower Foot-lb second = Horsepower (hp) 1 hp = 746 Watts 1 hp = ½ Columbus (who sailed in 1492) 1. How much horsepower is required to power a 100 Watt lightbulb? 2. A 1500 kg car has a profile that is 1.6 m wide and 1.4 m high. The coefficient of rolling friction is Calculate the drag force if the car travels at a steady 30 m/s (1/4Av 2 ) (504 N) 2. Calculate the force the car must exert against drag and friction. (798 N) 3. Calculate the power the engine must provide if 25% of the power is lost between the engine and the wheels. Horsepower Consider a 100 hp car engine that can go from 0 to 60 mi/hr in 20 seconds. A 400 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. 5

6 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? P = (200)(5)/3 = 333 W 333W/746W = 0.45 hp P = W t Work = Fd P = FDd Dt P = Fv Power and Calculus = F dx dt 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) = 1/3t 3 v = dx/dt v = t 2 v = (2)2 = 4 m/s a = dv/dt a = 2t a = 4 m/s 2 F = ma F = (0.5 kg)(4 m/s 2 ) = 2 N P = Fv = (2N)(4 m/s) Springs and Calculus The force in a spring is variable (F = -kx) Work = 0x F(x) dx Work = 0x -kx dx Work = - ½kx 2 Work = -DPE DPE = ½ kx 2 A particle experiences a force F(x) = 2x. a) Calculate the change in potential energy that the particle undergoes from 0 to 3 m. b) What kind of object might provide the force shown above? c) If the force is now F(x) = 2x 2, calculate the change in potential energy that the particle undergoes from 0 to 3 m. 6

7 Given the following force-distance graph, sketch the potential energy-distance graph. Given the following potential energy-distance graph, sketch the force-distance graph. 8. a) -12 J b) 0 J 10. a) -29 J b) 29 J kj 1.69 kj 1.07 kj J m/s (at 2 m) 4.0 m/s (at 4m) N, 0 N, -50 N 20. b) -12 N (y = 1 m) -48 N (y = 2m) 30. a) 9.8 X 10 5 J b) 1.96 X 10 4 W m 2 34.a) energy b) 1.8 X 10 9 J 36. a, b, c) 50 J (Conservative) 38. a) 400 N b) -2 J c) 22.4 m/s 36. a, b, c) 50 J (Conservative) 38. a) 400 N b) -2 J c) 22.4 m/s 42. a) 230 J b) 230 N c) 6.8 kw 44. a) 15.7 m/s b) 15.7 m/s A horizontal force pulls a 20.0 kg carton across the floor at a constant speed. The coefficient of kinetic friction, m k, is a. Calculate the work done moving the box 3.00 m. b Suppose the force is now at an angle of 30.0 o to the floor as shown in the figure. Calculate the force needed to pull the box across the floor at a constant speed. Be sure to consider any effects the rope may have on the normal force. c. Calculate the work done pulling the box 3.00 m under the conditions in (b). The following problems require calculus. The potential energy of a particle is defined as U = ax 3 bx 2. Determine the formula for the force acting on the particle. The potential energy of a particle is defined as U = U o sinbx. Determine the formula for the force acting on the particle. Calculate the work done from 1.00 m to 3.00 m for a particle that experiences a force F x = 5.0x Starting with the formula for the force of a spring, F spring = -ks, determine the formula for the potential energy stored in a spring. Integrate from 0 to x. 7

8 A 1.50 kg rocket from a craft store generates a thrust of 40.0 N. Using energy-work calculations, determine the speed at 10.0 m. Suppose the rockets only burns for the first 10.0 m. Calculate the total maximum height of the rocket. The following masses are attached to a pulley and cord as shown. Mass M is heavier than mass m. Using energy considerations, find an expression for the speed of either mass just before mass M hits the floor. 8

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