Question

If a pushing force making an angle alpha with horizontal is applied on a block of mass m placed on horizontal table and angle of friction is beta ,then minimum of force required to move the block is??

Answer 1

Answer on Question #44154, Physics, Mechanics | Kinematics | Dynamics

If a pushing force making an angle alpha with horizontal is applied on a block of mass $m$ placed on horizontal table and angle of friction is beta, then minimum of force required to move the block is??

Solution:

Then minimum of force required to move the block is such that its projection is equal to the force of friction :

$$F \cos (\alpha) = F _ {t}$$

From geometry :

$$N = m g - F \sin (\alpha)$$ $$F _ {t} = t g (\beta) N = t g (\beta) (m g - F \sin (\alpha)) = F \cos (\alpha)$$

Then $F = \frac{mg\sin(\beta)}{\cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta)} = \frac{mg\sin(\beta)}{\cos(\alpha - \beta)}$

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