Force and Motion II: Frictions on Inclines

Learning Goals

• Explore examples of friction on inclines.

• Build on previous discussions about flat surfaces and inclines with more focus on inclined planes.

Steps to Calculate Friction Force

1. Type of Friction

   • Static Friction: Object does not slide; tendency exists to slide.

   • Kinetic Friction: Object is sliding.

2. Direction of Friction

   • The frictional force always opposes the direction of sliding or the tendency to slide.

3. Magnitude of Friction

   • For static friction: $|f<em>{ ext{s}}| \leq \mu</em>s |N|$

   • For kinetic friction: $|f<em>{ ext{k}}| = \mu</em>k |N|$

   • Where:

     • $\mu_s$ = Static friction coefficient

     • $\mu_k$ = Kinetic friction coefficient

     • $N$ = Normal force

Example Problem: Box on an Incline

• Given:

  • Mass $m = 1 ext{ kg}$

  • Incline angle $\theta = 15^{\circ}$

  • Static friction coefficient $\mu_s = 0.3$

  • Kinetic friction coefficient $\mu_k = 0.2$

• Free Body Diagram (FBD)

  • Identify forces acting on the box:

    • Weight $W$

    • Normal force $N$

    • Frictional force $f$

Steps to Solve the Problem

1. Newton’s 2nd Law: Identify equations for x and y directions.

2. Calculate the Normal Force: Use $N = W imes cos(\theta)$

3. Calculate the Friction Force: Based on whether the box is static or kinetic.

Example 4: Forces on a Sledge on a Slope

• A tension force $T$ pulls the sledge while considering static and kinetic friction coefficients ($\mu<em>s$, $\mu</em>k$).

Clicker Questions

• Question 10: Analyze why the box is moving up the incline with the applied force.

• Question 11: Discuss what drives the sledge to slide.

  • Influential forces include the tension force $T$ and the weight component along the incline ($W_x$).

Tension and Weight on Inclines

• Variables at play in Forces:

  • Component of weight acting along the incline: $W_x = W \times sin(\theta)$

  • The opposing force of friction: $f = \mu |N|$

Additional Example Problems

• Loaded Penguin Sled Example (Questions 12-14):

  • Weight of sled: $70.0 N$

  • Inclination: $\theta = 21.0^{\circ}$

  • Static friction: $\mu_s = 0.290$

  • Kinetic friction: $\mu_k = 0.200$

  • Analyze forces to determine what prevents, initiates, or allows sliding movement depending on the situation.

Key Takeaways

• Understand distinction between static and kinetic friction as well as the conditions for each.

• Learn to apply Newton's laws to obtain the normal force and derive the frictional forces acting on objects on an incline.

• Proficiency in analyzing real-world examples involving forces on inclined surfaces enhances understanding of mechanics.

Steps to Calculate Friction Force

1. Type of Friction

   • Static Friction: Object does not slide; tendency exists to slide.

   • Kinetic Friction: Object is sliding.

2. Direction of Friction

   • The frictional force always opposes the direction of sliding or the tendency to slide.

3. Magnitude of Friction

   • For static friction:
     $|f<em>{s}| \leq \mu</em>s |N|$

   • For kinetic friction:
     $|f<em>{k}| = \mu</em>k |N|$

   • Where:

     • $\mu_s$ = Static friction coefficient

     • $\mu_k$ = Kinetic friction coefficient

     • $N$ = Normal force

Tension and Weight on Inclines

• Component of weight acting along the incline:
  $W_x = W \times sin(\theta)$

• Opposing force of friction:
  $f = \mu |N|$

Additional Example Problems

• Loaded Penguin Sled Example: Analyze forces to determine what prevents, initiates, or allows sliding movement depending on the situation.

Key Takeaways

• Understand the distinction between static and kinetic friction as well as the conditions for each.

• Learn to apply Newton's laws to obtain the normal force and derive the frictional forces acting on objects on an incline.

• Proficiency in analyzing real-world examples involving forces on inclined surfaces enhances understanding of mechanics.