friction

2010-05-30 9:08 pm
A block of mass 10kg tends to move up an inclined plane(30°) under the action of a horizontal force, if the coefficient of friction is 0.22 for all contact surfaces:
(i) Draw the free body diagram for the block.
(ii) Derive equations along the plane and normal to the plane.
(ii) Determine the force P that just enough to cause the block moving.upward.

回答 (1)

2010-05-30 9:25 pm
✔ 最佳答案
(i) There are 4 forces acting on the block:
- the weight of the block, acting vertically downward;
- the normal reaction, acting perpendicularly away from theb plane surface'
- the applied force, acting horizontally;
- firctional force, acting downward along the plane.

(ii) Along the plane:
F.cos(30) = 10g.sin(30) + Ff --------------------- (1)
where F is the horizontally applied force, g is the acceleration due to gravity, and Ff is frictional force

Normal to the plane:
10g.cos(30) + F.sin(30) = R ------------------ (2)
where R is the normal reaction

(iii) When the block just starts to move upward, frictional force acting on the block equals to limiting friction. Hence,
Ff = 0.22.R
Using equation (1); P.cos(30) = 10g.sin(30) + 0.22R ---------------- (3)
Substitute R from (2) into (3):
P.cos(30) = 10g.sin(30) + 0.22.(10g.cos(30) + P.sin(30))
solve for P


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