Section 2.2: Forces on Flat Surfaces

Objects on flat surfaces experience forces such as weight, normal force, friction, and applied forces.

Weight: The gravitational force acting on an object: \( W = mg \)

        Normal Force: The perpendicular contact force from the surface. On flat surfaces, \( N = W \) if no vertical forces other than weight.

        Friction: Resists motion along the surface.
        Static: \( f_s \le \mu_s N \)
Kinetic: \( f_k = \mu_k N \)

      

        Net Force on Flat Surface:
        \[
        F_{\text{net}} = F_{\text{applied}} - f
        \]
      

Example 1

A 10 kg block is pushed horizontally with 30 N on a frictionless surface. Find its acceleration.

\( a = F/m = 30/10 = 3 \text{ m/s²} \)

A 5 kg box on a surface with μk = 0.2 is pushed with 20 N. Find the friction and acceleration.

Normal force: \( N = mg = 5*9.8 = 49 \text{ N} \)

Friction: \( f_k = μ_k N = 0.2*49 = 9.8 \text{ N} \)

Net force: \( F_{\text{net}} = 20-9.8 = 10.2 \text{ N} \)

Acceleration: \( a = F_{\text{net}}/m = 10.2/5 \approx 2.04 \text{ m/s²} \)

A 15 kg crate is on a horizontal floor. If μk = 0.3 and you push with 50 N, find acceleration.
Determine the friction force acting on a 20 kg box when μs = 0.4 and μk = 0.3, pushed with 60 N.
A 12 kg block is at rest. Find the minimum force to start moving it if μs = 0.25.
A box experiences 100 N applied force, weight = 200 N, μk = 0.1. Find acceleration.
Draw free-body diagram for a 10 kg box pushed across a floor with friction.