Minimum Force Required to Slide a Body on a Rough Horizontal Plane
Let a body A of weight W is resting on a rough horizontal plane B, as shown in Fig. 1.19. Let an effort P is applied at an angle θ to the horizontal, such that the body just begins to move. From Fig. 1.19, we find that
![](data:image/png;base64,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)
For P to be minimum, cos (θ - ϕ) should be maximum, i.e.
cos (θ-ϕ)=1 or θ-ϕ=0 or θ=0
In other words, the effort P is minimum when its inclination (θ) with the horizontal is equal to the angle of friction (ϕ).
Let a body A of weight W is resting on a rough horizontal plane B, as shown in Fig. 1.19. Let an effort P is applied at an angle θ to the horizontal, such that the body just begins to move. From Fig. 1.19, we find that
For P to be minimum, cos (θ - ϕ) should be maximum, i.e.
cos (θ-ϕ)=1 or θ-ϕ=0 or θ=0
In other words, the effort P is minimum when its inclination (θ) with the horizontal is equal to the angle of friction (ϕ).
video not available
ReplyDeleteAdd SOM ,VIBRATION and TOM subjects also
ReplyDelete