If a man pulls a square-shaped box of mass 10 kg with the force of 50 Newton and body start to accelerate in the direction of force with 2 m/s². What will be the value of the coefficient of friction and the type of frictional force?

CONCEPT:

Friction Force: It is a kind of resisting force that acts between two contact bodies to avoid relative motion between them.

• It is formed due to the close interaction of charged particles at the surface of the bodies due to electromagnetic forces.
• Mathematically it is represented as Friction force = μ N.
• Where N = normal force = m × g
• Normal force: It is a force that is exerted by the surface perpendicular to the body. It is a component of the contact force.

Frictional forces are of two kinds:

1. Static friction (f_s): When two bodies do not slip on each other, the force of friction is static friction. It can change its value until its max. F_max ≥ f_s
2. Kinetic Friction (f_k): When two bodies slip over each other the force of friction is called kinetic friction.

• Coefficient of Kinetic friction (μ_k) < Coefficient Static friction (μ_s).

• Force: It is a kind of push or pull of a body.
  • Force produces acceleration in a body.
  • F = m × a [m = mass of the body, a = acceleration in a body]
• Free Body Diagram: It is an illustration to visualize the forces and resultants of each body respectively

CALCULATION:

• Given, Mass of the body (m) = 10 kg, Normal force = mg = 10 × 10 = 100 N
• Coefficient of friction (μ) = ?
• Free body diagram of the box is

Since the body accelerates in the direction of the force.

The laws of motion in the horizontal line is

F - μ_k N = ma

⇒ 50 – (μ_k × 100) = 10 kg × 2 m/s²

⇒ μ _k = 0.3

Since the body is already in motion the kinetic friction is working.