A pulling force making an angle θ to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is ϕ, the magnitude of the force required to move the body is equal to:

A block of mass m lying on a horizontal surface (coefficient of static friction = μs) is to be brought into motion by a pulling force F. At what angle θ with the horizontal should the force F be applied so that its magnitude is minimum? Also find this minimum magnitude.

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ>μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1=mg (sinθ−μcosθ) to P2=mg (sinθ+μcosθ), the frictional force f versus P graph will look like

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A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in figure. The coefficient of kinetic friction is µK. Then, the block's acceleration 'a' is given by:(g is acceleration due to gravity)