Experiment No - 5: Determining Coefficient of Friction (PDF)

# **EXPERIMENT No - 5** ## **OBJECT:** - Determination of coefficient of friction using inclined plane set up. ## **APPARATUS:** - Inclined plane - Wooden Box - Cord with pan - Weights etc. ## **FORMULA:** $µs = \frac{W1-Wsinθ}{Wcosθ}$ ## **FIGURE:** - **Pulley** - **Cord** - **Inclined Plan...

# **EXPERIMENT No - 5** ## **OBJECT:** - Determination of coefficient of friction using inclined plane set up. ## **APPARATUS:** - Inclined plane - Wooden Box - Cord with pan - Weights etc. ## **FORMULA:** $µs = \frac{W1-Wsinθ}{Wcosθ}$ ## **FIGURE:** - **Pulley** - **Cord** - **Inclined Plane** - θ - b - h - **Weight (W) Inclusive of box** - **Weight (W1) Inclusive of Pan** ## **THEORY:** ### **Laws of Friction:** The laws of dry friction (Sometimes called Coulomb friction) may be stated as follows: 1. If friction is neglected, the reactions are always normal to the surface incontact. 2. Friction always acts to oppose the relative motion of the free body (or its tendency to move) and it is tangent to the surfaces in contact. 3. If static friction is acting, the value of the friction force may vary from zero to its maximum available value adjusting itself to the resultant force tending to cause motion. - **The maximum available Value of static friction (i.e. the limiting friction when motion impends)is equal to 1.1.s N where 1..ts is the coefficient ofstatic friction & N is the normal force.** - **If motion occurs, the kinetic friction force always acts at its constant value of14 N where ilk is the coefficient of kinetic friction & N is the normal force.** - **The angle between the total reaction and its normal component when limiting friction is acting is called the angle of friction. The tangent of this angle is equal to the coefficient of friction.** ## **i) Laws of Friction :** At a fixed angle of inclination θ, the suspended mass is increased until the block is at the verge of upward slippage, i.e., in the state of impending motion. Refer to the free-body diagram of the block at such a state as shown above for equilibrium. **FBD of pan:** +↑$Fy = 0$ : T = $W1$ ... (1) **FBD of block:** +↑$Fy = 0$ : N = $Wcosθ$ ... (2) +↑$Fx = 0$ : T = $μsN - Wsinθ = 0$ ... (3) (1) and (2) in (3)gives $W1-μs. Wcose - Wsinθ = 0$ $μs = [W1-Wsine] / Wcose$ ## **PROCEDURE:** 1. Set the incline plane of some suitable angle. 2. Note the weight of box and pan. 3. Put some weight say 50 gm in box and note W inclusive of weight of box. 4. Go on adding weights, in pan till the box just starts moving up on the incline. 5. Note W1 inclusive of weight of pan & weight added. 6. Increase weight W & repeat steps 4 & 5. ## **OBSERVATION:** |Sr. No.|Weight (W)|Weight (W1) |Angle (θ)|$µs = \frac{W1-Wsinθ}{Wcosθ}$ | |---|---|---|---|---| |1| | | | | |2| | | | | |3 | | | | | |4 | | | | | |5| | | | | ## **SAMPLE CALCULATION:** $µs = \frac{W1-Wsinθ}{Wcosθ}$ Average $µs$ ## **RESULT:** - The coefficient of friction between wood (base of box) &glass (top of inclined plane) is, $µs=$ ## **CONCLUSION:** - The critical angle of inclined plane, $Ocritical = {tan^-1}{µs} =$