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Solving Inclined Plane Problems

Solving Inclined Plane Problems. Inclined Plane Problems. First you have to determine if the plane has friction or not. If there is no friction, the following is true: Work in = Work out Fe x de = Fr x dr Remember that Fr = the weight of the object. If There is no Friction. Fe. de. dr.

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Solving Inclined Plane Problems

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  1. Solving Inclined Plane Problems

  2. Inclined Plane Problems • First you have to determine if the plane has friction or not. • If there is no friction, the following is true: • Work in = Work out • Fe x de = Fr x dr • Remember that Fr = the weight of the object

  3. If There is no Friction Fe de dr Fr Fe x de = Fr x dr same as weight

  4. Sample Problem #1 A 50 N object is being pushed up a frictionless ramp. The ramp is 5 m long and 2 m high. What is the work Input? Work input = Fe x de Do you know Fe? no You do know the work output = Fr x dr Work out = 50N x 2 m = 100 J Work in = work out, so Work input = 100 J

  5. Sample Problem #2 A 200 N object is being pushed up a frictionless ramp that is 6 m long and 3 m high. Calculate the effort force. Work in = Work out Fe x de = Fr x dr Fe x6m = 200N x 3m Fe = 100N

  6. Sample Problem #3 A 5 m long frictionless ramp makes a 25 degree angle with the ground. A 1500 N object is being pushed up the ramp. What is the work input? In this problem, there is no height or Fe. All you know is The de, the weight(Fr), and an angle.

  7. Sample Problem #3 A 5 m long frictionless ramp makes a 25 degree angle with the ground. A 1500 N object is being pushed up the ramp. What is the work input? First, you need to find the height since there is no way to calculate the Fe. Sin 25degrees = height / length Sin 25 degrees = height/ 5m height = 2.1 m

  8. Sample Problem #3 A 5 m long frictionless ramp makes a 25 degree angle with the ground. A 1500 N object is being pushed up the ramp. What is the work input? Now you can calculate the work output Work out = Fr x dr = 1500 N x 2.1 m (height) = 3150 N Work in = Work out = 3150 N

  9. Inclined Plane with Friction Fe de Ff dr F ll Fr F ⊥ Fw Fll

  10. Sample Problem #4 A 1000 kg object is being pushed a 300 m ramp that has friction and makes a 17.5 angle with the ground. Calculate the Work input if the coefficient of Friction is 0.25. Assume that there is no acceleration First Work in does not equal work out so you cannot just find the height x weight. You do need to find the weight in order to finish the problem. Weight (Fr) = 1000 kg x 9.8 = 9800 N

  11. Sample Problem #4 A 1000 kg object is being pushed a 300 m ramp that has friction and makes a 17.5 ° angle with the ground. Calculate the Work input if the coefficient of Friction is 0.25. Assume there is no acceleration. Now you have to find the F parallel and F perpendicular. F parallel Sin 17.5 °=F parallel / 9800 N F parallel = 2950 N F perpendicular Cos 17.5 ° = F perpendicular / 9800 N F perpendicular = 9350 N Ff = µF perpendicular = (0.25)(9350)= 2340N

  12. Sample Problem #4 A 1000 kg object is being pushed a 300 m ramp that has friction and makes a 17.5 ° angle with the ground. Calculate the Work input if the coefficient of Friction is 0.25. Assume there is no acceleration. Next, you can calculate the Effort Force Fe = Ff + F parallel = 2340N + 2950N Fe = 5290N Work in = Fe x de Work in = 5290N x 300 m Work in = 1.6 x 106 J

  13. Sample Problem #4 A 1000 kg object is being pushed a 300 m ramp that has friction and makes a 17.5 ° angle with the ground. Calculate the Work input if the coefficient of Friction is 0.25. Assume there is no acceleration. What is the work output? First find dr Sin 17.5degrees = dr / 300 m dr = 90.2 m Work out = Fr x dr Work out = 9800 N x 90.2m Work out =8.8 x 105 J

  14. Sample Problem #4 A 1000 kg object is being pushed a 300 m ramp that has friction and makes a 17.5 ° angle with the ground. Calculate the Work input if the coefficient of Friction is 0.25. Assume there is no acceleration. What is the MA, the IMA, and the Efficiency of this ramp? MA = Fr / Fe IMA = de/dr MA = 9800 N/ 5290N IMA = 300 m / 90.2 m MA = 1.8 IMA = 3.3

  15. Sample Problem #4 A 1000 kg object is being pushed a 300 m ramp that has friction and makes a 17.5 ° angle with the ground. Calculate the Work input if the coefficient of Friction is 0.25. Assume there is no acceleration. What is the MA, the IMA, and the Efficiency of this ramp? Efficiency = Work out/ Work in or Eff = MA/ IMA Eff = 8.8 x 105 J/ 1.6 x 106 J Eff = 1.8/3.3 Eff = .55 x 100 Eff = .55 x 100 Eff = 55% Eff = 55%

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