Understanding Friction: How to Control Motion on an Incline

We analyze the forces acting on a loaded apple box weighing 80 N, resting on an inclined plane with an angle of 20°. This video tutorial will guide students through the intricate play between static and kinetic friction and their impacts on motion.

In this tutorial, you'll learn:

1. How to compute the minimum force needed to keep the box from sliding down the incline.
2. The necessary force to initiate the box's ascent up the incline.
3. The exact force required to maintain the box's movement up the plane at a constant speed.

Detailed Explanation and Calculations:

Introduction to Forces on an Incline:

• Start by breaking down the gravitational force (weight) into components along and perpendicular to the incline.

Understanding Friction:

• We consider static friction (μₛ = 0.25) and kinetic friction (μₖ = 0.15) coefficients to understand their roles.

Part A: Preventing the Box from Slipping Down

• Equilibrium Analysis: We assess the scenario where the box is on the verge of slipping downward.
  • Calculation:The force equation along the plane is Fₘ - 80 sin(20°) + fₛ = 0, where fₛ is the static friction.
  • Maximum static friction force fₛ = μₛ × N = 0.25 × 80 cos(20°).
  • Rearranging the equation, Fₘ = 80 sin(20°) - μₛ × 80 cos(20°).
  • Calculating with values, Fₘ = 80(sin(20°) - 0.25 cos(20°)) ≈ 8.6 N.

Part B: Starting the Box Moving Up the Plane

• Overcoming Static Friction: Here, the static friction opposes the initial motion of ascending.
  • Calculation:Fₘ - 80 sin(20°) - fₛ = 0.
  • Rearrange to Fₘ = 80 sin(20°) + μₛ × 80 cos(20°).
  • Calculate Fₘ = 80(sin(20°) + 0.25 cos(20°)) ≈ 46 N.

Part C: Moving the Box Up the Plane at Constant Velocity

• Dealing with Kinetic Friction: Here, kinetic friction comes into play since the box moves.
  • Calculation:Fₘ - 80 sin(20°) - fₖ = 0, where fₖ = μₖ × N.
  • Rearrange to Fₘ = 80 sin(20°) + μₖ × 80 cos(20°).
  • Calculate Fₘ = 80(sin(20°) + 0.15 cos(20°)) ≈ 39 N.

This tutorial is ideal for Class 11, Class 12, and AP Physics students, equipping them with practical skills to solve problems involving forces and friction. By the end of this video, you'll have a thorough understanding of how to manipulate and calculate forces to control motion on an inclined plane effectively.