Materials Testing Lab: Coefficient of Friction ($\mu$)
Use the Inclined Plane apparatus to determine the **Coefficient of Static Friction ($\mu_s$)** using the **Angle of Repose** method, and calculate the **Coefficient of Kinetic Friction ($\mu_k$)** when the block is sliding.
Mission Briefing: Key Equations & Concepts
â–¼At the **Angle of Repose ($\theta_R$)** (the angle where sliding just begins): $$ \mu_s = \tan\theta_R $$
If the object starts from rest and slides a distance ($s$) in time ($t$): $$ a = \frac{2s}{t^2} $$
Derived from Newton's 2nd Law ($F_{net}=ma$): $$ \mu_k = \frac{g \sin\theta - a}{g \cos\theta} $$
Experiment 1: Angle of Repose ($\mu_s$) Finder
Adjust the angle until the block **just begins** to slide (simulating $\mu_s = \tan\theta_R$).
Experiment 2: Kinetic Friction ($\mu_k$) Calculation Challenge
Given the motion data ($s$ and $t$), calculate the coefficient of kinetic friction ($\mu_k$).
The **Angle of Repose ($\theta_R$)** is the steepest angle an inclined plane can make with the horizontal before an object placed on it starts to slide. At this point, the force pushing the object down the ramp ($mg \sin\theta$) is exactly balanced by the maximum static friction force ($\mu_s mg \cos\theta$), leading to the simple result $\mu_s = \tan\theta_R$.
Advanced Friction Concepts (11th Std)
The **coefficient of static friction ($\mu_s$)** is generally always **greater** than the **coefficient of kinetic (sliding) friction ($\mu_k$)**. This is why it takes more force to get an object moving than to keep it moving.
Friction is a **non-conservative force** because the work done against it depends on the path taken. The energy lost due to friction is typically converted into **heat energy**.
The coefficient of friction does **not** depend on the **mass** or the **area** of contact, only on the nature (material) of the two surfaces.
