A man pulls up a box of mass 50kg using an inclined plane of effective length 3m onto platform 1.5m high at uniform speed. If the frictional force between the box and the plane is 80N, draw the diagram of all the forces acting on the box when in motion and calculate the; i. minimum effort the applied in pulling up the box ii. velocity ratio of the plane iii. mechanical advantage of the plane iv. efficiency of the plane V. energy lost in the system vi. total power developed by the man given that the time taken to raise the box onto the platform is 40s. [Take g=10ms)
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Answers
Answer:
Explanation
(a) Work is done whenever a force moves a body through a certain distance in the direction of the force. It is measured in joule and it is a scalar quantity.
(i) Minimum effort (E) applied in pulling up the box = F = mgsinθ = 100 + 700 sin30° = 100 + 700 x 0.5 = 100 + 350=450N.
(ii) Velocity ratio (V.R) of the plane = 1/sinθ - 5/2.5 = 2
(iii) Mechanical advantage of the plane (M.A) = L/E = 1.56 .
(iv) Efficiency of the plane = M.AV.R x 100%
= 1.562 x 100% = 78%
(v) Energy lost in the system = work input - work output = (450 x 5) - (700/2 x 5) = 2250 - 1750 = 550J.
(vi) Work output of the man = mgh = 70 x 10 x 2.5 = 1750J
(vii) Total power developed by the man
= work done by efforttime = 450×550 = 45 watts
Answer:
Formula of Resultant Force
If one force is acting perpendicular to another, the resultant force is determined by using the Pythagorean theorem. The Resultant force formula is given by, FR = F1 + F2 + F3. Where. F1, F2, F3 are the three forces acting in the same direction on an object.