At a Mercedes Benz dealership a hydraulic lift is used to jack a one of the cars
ID: 2016610 • Letter: A
Question
At a Mercedes Benz dealership a hydraulic lift is used to jack a one of the cars which weighs 970kg 10 cm off the floor. The output piston has a diameter of 18 cm, and the input force is 250 N.(a) What would be the area of the input piston?
m2
(b) What would be the work done in lifting the car 10 cm?
J
(c) say the input piston actually moves 13 cm in each stroke, how high would the car move up for each stroke?
m
(d) How many strokes would be required to jack the car up 10 cm? (Include fractions of a stroke in your answer).
(e) determine the combined work input of all of the strokes.
J
Explanation / Answer
Given that the mass of car is m = 970 kg Input force is Fi = 250 N Diameter of output pistion is Do = 18 cm Radius fo output pistion is Ro = 0.09m ---------------------------------------------------------- (a) From Pascal's principle, Fi / Ai = Fo / Ao Ai = ( Fi / Fo )Ao = (Fi / mg)Ro2 = 6.7x10-4 m2 (b) Work done lifting the car is W = Fo*do = mg*0.10 m = 950.6 J (c) Since the work done by output pistion is equal to input pistion. Fo*do = Fi*di do = Fi*di / mg = 0.00342 m = 0.342 cm (d) Number of strokes would be required to jack the car up 10 cm is N = 10 cm / 0.342 cm = 29.24 ˜ 29 stokes (e) The work done by input pistion is W = Fi*di = Fo*do = 950.6J = 0.342 cm (d) Number of strokes would be required to jack the car up 10 cm is N = 10 cm / 0.342 cm = 29.24 ˜ 29 stokes (e) The work done by input pistion is W = Fi*di = Fo*do = 950.6JRelated Questions
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