Lawn mover - pulling or pushing
When we pull a lawn mover, the force exerted is directed outwards from the ground along the lawn mover handles. The force F applied through hands, is inclined at an angle Ф to the (horizontal) ground. Let the lawn mover have a mass m.
The normal reaction N of the ground on the lawn mover will be
N = m g - F SinФ
Due to reduced normal reaction, the friction (static or kinetic) Ff between the lawn mover and the ground will be reduced from μ m g to μ (m g - F Sin Φ). Hence it is easy to move it along the ground. The net force F Cos Φ - μ (mg - F Sin Φ) along the horizontal helps the movement of the lawn mover smoothly. Only thing is one needs to move backwards.
net horizontal force = F (cos Φ +μ Sin Φ) - μ m g to drive the lawn mover
Minimum Force to be applied by us to just move it, F = μ m g /(Cos Φ + μ Sin Φ)
When we push the lawn mover along the inclined handle, the force applied is directed into the ground. The normal reaction on the lawn mover by the ground is now = N = (m g + F Sin Φ). Hence the force of kinetic or static friction increase to Ff = μ (m g + F Sin Φ). So it is more difficult to move the lawn mover along the ground. The force F Cos Ф must be more than Ff.
the net horizontal force to drive lawn mover = F Cos Φ - μ mg - μ F Sin Φ
= F (Cos Φ - μ Sin Φ) - μ m g
Clearly this force is much less compared the force available in case of pulling the lawn mover.
Minimum Force to be applied by us to move it = F = μ m g / (CosΦ - μ SinΦ)
Clearly this is more than in case of pulling the lawn mover.