Question

A home-owner pushes a lawn mower across a horizontal patch of grass with a constant speed by applying a force ‘P’. The arrows in the diagram correctly indicate mower. Which of the following relations among the various force magnitudes W, f, N, P is correct?

A. P > f and N > W
B. P < f and N = W
C. P > f and N < W
D. P = f and N > W

Answer 1

Hint: The four magnitudes of force are given, each facing a particular direction. It is based on the application of friction force and the components of normal applied force. Friction occurs only between two touching surfaces.

Complete step-by-step answer:
Friction is a kind of force that resists the relative motion of solid surfaces or fluids or materials that are sliding against each other. It is not a fundamental force but a result of electromagnetic attraction between charged particles within the touching surfaces. The equation or formula for the friction force can be written as,
$f=\mu \times N$
Where, ‘f’ is the frictional force
‘μ’ is the coefficient of friction and
‘N’ is the normal force.
If an object is moving, the friction acts perpendicular and proportional to the normal force. It is independent of the area of contact and depends upon the nature of the surface.
Now considering the question, if the applied force of the house-owner is greater than the friction force ‘f’, the lawn mower may move forward because the horizontal component of the normal force must be greater than the frictional force. Which means P > f.
And also, the grass will get cut if N > W because the vertical component of the normal force is in the direction of W.
Therefore, the correct answer for the given solution is option (A).

Note: Friction always acts opposite to the direction of normal force and it has four types. They are static, sliding, rolling and fluid friction. The statis, sliding and rolling occurs only between two solid surfaces whereas, fluid friction occurs in liquids and gases.