工程科學應力應變題 Ex4 ?

冰封的人

2007-03-28 6:02 am

Acceleration due to gravity = 10 ms-2;
Calculation steps should be clearly shown;
Answers correct to two decimal places.

4. An object of mass 10kg rests on a smooth plane inclined at an angle of 30o to the horizontal. Find the horizontal force in Newton which will keep the body in equilibrium. Find also the least force required to keep the body in equilibrium and state the direction in which such a force must be applied.

回答 (1)

魏王將張遼

2007-03-28 7:25 am

✔ 最佳答案

The scenario can be figured out by the diagram below:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Phy/Static-1.jpg

From the diagram, we can see that the block can be maintained at stationary if the components along the horizontal direction are balanced (since the plane is smooth), i.e.
F cos 30° = 100 sin 30°
Hence we have:
F = 100 tan 30°
= 57.7 N (corr. to 1 d.p.)
And for the least force required, it can be achieved if the force is solely for balancing the component of the weight of the block along the inclined plane and for the normal direction, the plane will provide the reaction force to support the block.
Therefore:
Minimum force required = 100 sin 30° = 50 N in the direction up the inclined plane

2007-03-28 00:03:47 補充：
For the horizontal force, if correct to 2 d.p., it is 57.74 N.(Sorry for overlooking the instructions.)

參考: My Physics knowledge

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