Consider the first case. If we push the body from the top left corner, the force will have two components one in horizontal direction and another in vertical direction. The components in horizontal direction is Fcosθ which will help the person to push the body. While the vertical component Fsinθ will add up to the weight of the body. This will increase the normal force N i.e. N=mg+ Fsinθ. The pushing force will then become Fcosθ=μN=μ (mg+ Fsinθ), where μ is the coefficient of friction.
Now if we consider the second case, when the person is pushing the body from behind with the force F, the vertical component Fsinθ will be in upward direction and horizontal component Fcosθ will be in the direction of force. This vertical component will reduce the normal force N i.e. N= mg – Fsinθ. Hence, pushing force Fcosθ= μ(mg - Fsinθ). That is why pushing a body from behind is easier.
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