Section 2.2: Forces on Level Surfaces

This section focuses on objects on horizontal surfaces. We analyze the forces acting on them and how to compute acceleration using Newton’s second law.

Normal Force (\( F_N \)):

The upward support force exerted by a horizontal surface on an object. For a flat surface without vertical acceleration:

\( F_N = mg \)

Where \( m \) = mass of object, \( g \) = acceleration due to gravity (9.8 m/s²).

Friction Force (\( f \)):
  • Static Friction: Prevents motion, \( f_s \leq \mu_s F_N \)
  • Kinetic Friction: Opposes motion, \( f_k = \mu_k F_N \)

\( \mu_s \) and \( \mu_k \) are the coefficients of static and kinetic friction respectively.

Net Force on Horizontal Surface:

\( F_{\text{net}} = F_{\text{applied}} - f_k \)

Then, acceleration is \( a = \frac{F_{\text{net}}}{m} \)

Example 1

A 10 kg block is pushed with 50 N across a horizontal surface. The coefficient of kinetic friction is 0.2. Find the acceleration.

Normal force: \( F_N = mg = 10*9.8 = 98 \text{ N} \)

Friction force: \( f_k = \mu_k F_N = 0.2*98 = 19.6 \text{ N} \)

Net force: \( F_{\text{net}} = 50 - 19.6 = 30.4 \text{ N} \)

Acceleration: \( a = F_{\text{net}}/m = 30.4 / 10 = 3.04 \text{ m/s²} \)

Example 2

A 5 kg box experiences 15 N applied force to the right and friction of 5 N. Find acceleration.

Net force: \( F_{\text{net}} = 15 - 5 = 10 \text{ N} \)

Acceleration: \( a = F_{\text{net}}/m = 10/5 = 2 \text{ m/s²} \)

Practice Problems

  1. A 12 kg crate is pulled with 60 N; friction = 15 N. Find acceleration.
  2. A 20 kg box is pushed with 100 N; friction = 25 N. Compute net force and acceleration.
  3. A 10 kg block is on a surface with µk = 0.3. Find friction force if g = 9.8 m/s².
  4. A 5 kg object is pulled with 25 N while friction = 5 N. Find acceleration.
  5. A sled of 15 kg is pulled with 40 N, friction = 10 N. Determine acceleration.
  6. A 8 kg box moves on horizontal surface with friction 8 N, applied force = 32 N. Compute acceleration.
  7. A 6 kg block experiences 18 N right, 6 N friction left. Find net acceleration.
  8. A 3 kg object moves with applied 12 N; friction = 3 N. Find acceleration.
  9. A 10 kg box is pulled with 50 N; friction = 20 N. Find acceleration.
  10. A 4 kg block is pulled with 24 N on frictionless surface. Find acceleration.
  11. A 7 kg box experiences applied 28 N, friction = 14 N. Find net force and acceleration.
  12. A 50 kg crate is pushed with 200 N; friction = 50 N. Find acceleration.
  13. A 15 kg object has µk = 0.25. Compute kinetic friction.
  14. A 20 kg block is pushed by 80 N on a surface; friction = 16 N. Find acceleration.
  15. A 5 kg object is pulled by 30 N; friction = 10 N. Determine acceleration.
  16. A 10 kg box is at rest. Find net force if pushed with 40 N; friction = 8 N.
  17. A sled of 8 kg pulled by 32 N; friction = 8 N. Compute acceleration.
  18. A 12 kg crate is pulled with 60 N; friction = 12 N. Find acceleration.
  19. A 7 kg box is pushed with 28 N; friction = 14 N. Find net acceleration.
  20. A 6 kg object is pulled with 24 N; friction = 6 N. Find acceleration.
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