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Worksheet8.1 Work, Energy, and Power

Work Done by a Constant Force

In Physics, the word "work" takes on a different meaning from the one commonly used.Workis defined as a force applied through a distance. Work done on an object by a constant force is the product of the object’s displacement and the force acting parallel to the displacement. In mathematical terms

Work = Fdwhere: F=force (N) and d=distance (m)

The SI unit for work is thejoule(J). One joule is the product of one Newton and one meter, or a joule is a one-Newton force applied through one meter, J = Nm. For example, if a girl pushes a box with a 5.0-Newton horizontal force, and the box travels 2.0 meters in the direction of her push, the amount of work done is (5.0 N)(2.0 m) = 10 joules.

While the equation is valid for forces applied parallel to the direction of travel of an object, non-parallel forces present a problem. To calculate the work done by a force applied in a direction that is not parallel to an object’s displacement, we must calculate the component of the force applied in the parallel direction. To do this, we can use Equation

W = F cosθ x

whereF is the force, x is the displacement, and θis the angle between the directions of the force and the net displacement.

F = maKE = ½ mv2

Gravitational Potential Energy = weight x heightsince w=mgPE = mgh

Power = Work / Time Power = (Force x Distance) / Time

Power = mgh/t Power = Fv

Directions: Analyze and solve the following problems deligently. Show your solutions. Identify the given, the unknown and illustrate the problem.

  1. A Gain Lupper pulls a 10-kg luggage along a level floor at the airport for 5m by exerting a force of 20N at an angle of 300 with the horizontal shoulder through a vertical distance of 1.5m and carries it for another 5m. How much work does he do in a) pulling, b) lifting, and c) carrying the luggage in his shoulder?
  2. Lorenzo pulls a toy 3.0m across the floor by a string, applying a force of 0.50N. During the first meter, the string is parallel to the floor. In the next two meters, the string makes an angle of 30o with the horizontal direction. What is the total amount of work done by Lorenzo on the toy?
  3. After finishing his lab report, Rafael pulls his 75kg body out of the study room chair and climbs up the 5.0m high flight of stairs to his bedroom. How much work does Rafael do in going to his bedroom?
  4. Marvin applies a horizontal force of 50N to move a box a distance of 4m along a level floor. How much work is done by him? What force did he applied at an angle 60o and 90o?
  5. How much work is done on a 100N boulder that you can carry horizontally across a 10m room?
  6. How much work is done on a 100N boulder if you lift it 1m? What power is expended if you lift the boulder a distance of 1m in a time of 1s? What is the gravitational potential energy of the boulder in the lifted position?
  7. A force of 800 Newtons is needed to push a car across a lot. Two students push the car 40 meters. How much work is done?
  8. How much work is done in lifting a 60Kg crate a vertical distance of 10 meters?
  9. A 1000 N mountain climber scales a 100 m cliff. How much work is done?
  10. You are using 50 N of force to push an empty cart down the school hall. Your friend, who weighs 800 N, jumps on the cart and wants to be taken for a ride. You push your friend down the hall for 20 meters before being caught by the Principal. How much work did you do pushing your friend on the cart?
  11. A 1500 kg car accelerates uniformly from rest to a speed of 18m/s in 4.59 s.a) Find the WORK done by the NET FORCE on the car during this time interval. (Answer in units of J.)b) Find the average power DELIVERED by the NET FORCE to the car in this time interval. (Answer in units of w.)c) What is the instantaneous power delivered by the NET FORCE to the car at 2 s? (Answer in units of w.)
  12. A car engine exerts a driving force of 12,oooN. What is the work donw by the car in travelling a distance of 500m?
  13. How much work is done in lifting a 600kg sack of rice to a vertical distance of 10m?
  14. Sean push against a rock with a force of 100N for 20s. If the rock does not move, how much work in joules did he done?
  15. Eijay pushes his wooden cart with a force of 25N through a distance of 12m. What is the work done by Eijay?
  16. A 2kg ball falls freely from a height of 3m. What is its kinetic energy in joules when it hits the ground?
  17. What is the useful work done by a pump which discharges 2 000 liters of fuel oil into a tank 15 m above the intake? Fuel oil weighs 2 119 kg/m3?
  18. Under the action of certain forces, a drum of liquid detergent moves up a 30o inclined plane to the delivery truck. The weight W is equal to 180N. FN is the normal force (perpendicular to the plane) and is equal to 90N. What is the work done by force FN when the drum moves 4m up the plane?
  19. A force F of 102N is applied in pushing a 700N narra table continuously at an angle of 60o. What is the velocity of the table after it has been moved 7 m from rest? (neglect friction)
  20. Calculate the potential energy gained by 50 000kg train after climbing a 20m hill?
  21. A bullet moves with a velocity of 600 m/s and has gained a kinetic energy of 900 J. Calculate its mass.
  22. An 8hp crane lifts 100kg piece junk metal in 15 s. To what distance was the load lifted?
  23. A 950kg car has a motor that can deliver a power of 3.36x104 J/s to move the car forward. The maximum constant speed of the car on the level road is 100km/h. Find the retarding force that acts on the car?
  24. A ladder that is 3.97 m long leans against a window. The ladder makes an angle of 650 with the ground. If Lemuel, weighing 50kg goes up the ladder with a load of 2kg on his shoulder, how much work does he do?
  25. Mark and Izalyn climb a hill 70m high. Izalyn follows a winding path to the top while Mark takes the path that goes straight up 60o from the horizontal. What is the amount of work done by Mark and Izalyn suppose Izalyn is 40kg and Mark is 50kg?
  26. A machine produces 4000 Joules of work in 5 seconds. How much power does the machine produce?
  27. A box that weighs 1000 Newtons is lifted a distance of 20 meters in 10 seconds. How many kilowatts of power are produced?
  28. Jules is 70kg he climbs a flight of stairs 5.5m high in 5s.Calculate the power output in watts and in horsepower.
  29. Danielle is driving her car at a constant velocity of 80km/h on skyway. What is the power output of the car engine if the total resistance of friction between road and tires is 850N?
  30. A small electric motor is used to lift a 100N water to a tank 4 m above the ground in 10s. Calculate the useful power output of the motor.
  31. A 90 kW electric kettle boils sufficient amount of water for 10 mugs of coffee in 10 min. How much will it cost to boil this amount of water on two separate occasions? Assume that electric energy costs P8.00/kWh.
  32. What power is employed in lifting a 50 kg weight to a height of 20m in 1 min?
  33. What power is needed by a crane to raise a 400kg crate to a height of 16 m in one minute.
  34. Franco carries a 12 kg knapsack while climbing a mountain. After 20 minutes, he is 6 m above the foot of the mountain. If Franco weighs 6.8x102 N, how much power had he used?
  35. Bryan exerts a 120N force on a wheelbarrow loaded with garden soil. If he pushes it 50m at a constant speed for 20 s, what is his power if his speed is doubled?

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