To study the relationship between the force of limiting friction and normal reaction and to determine the coefficient of friction between a wooden block and a horizontal surface.

• A wooden block with hook
• A horizontal wooden board/table
• Weight box (standard masses: 50g, 100g, etc.)
• Spring balance (0-5N)
• Thread
• Frictionless pulley
• Laboratory stand with clamp
• Weighing balance

Friction is the force that opposes the relative motion between two surfaces in contact. When an object is placed on a horizontal surface, it experiences a normal reaction force perpendicular to the surface and equal in magnitude to the weight of the object.

There are three types of friction:

1. Static Friction: The friction that exists between stationary surfaces in contact.
2. Limiting Friction: The maximum value of static friction, beyond which the object begins to move.
3. Kinetic Friction: The friction that exists between moving surfaces in contact.

The laws of solid friction state that:

1. The force of friction is directly proportional to the normal reaction between the surfaces in contact.
2. The force of friction is independent of the apparent area of contact between the surfaces.
3. For low velocities, kinetic friction is independent of the relative velocity between the surfaces.

Mathematically, the relationship between limiting friction \(F\) and normal reaction \(R\) is given by:

Where \(\mu\) is the coefficient of friction between the two surfaces, which depends on the nature of the surfaces in contact.

1. Measure the mass of the wooden block using the weighing balance and record it.
2. Place the wooden block on the horizontal surface.
3. Attach one end of the thread to the hook on the wooden block.
4. Pass the other end of the thread over the frictionless pulley fixed at the edge of the table.
5. Attach the spring balance to the free end of the thread.
6. Apply a small horizontal force by gently pulling the spring balance and slowly increase the force.
7. Note the reading of the spring balance at the instant when the block just begins to move. This reading gives the limiting force of friction for the given normal reaction.
8. Place a known weight on top of the wooden block to increase the normal reaction.
9. Repeat steps 6 and 7 for different weights placed on the block to obtain different values of normal reaction.
10. Record all observations in the table.
11. Plot a graph between the force of limiting friction (F) on the y-axis and the normal reaction (R) on the x-axis.
12. Calculate the coefficient of friction for each observation and find the average value.

Mass of the wooden block (M) = ______ g = ______ kg

Acceleration due to gravity (g) = 9.8 m/s²

Weight of the wooden block (W = Mg) = ______ N

For each observation:

1. Calculate the normal reaction (R):
   \[ R = mg \]
   where m is the total mass (block + added mass) in kg, and g = 9.8 m/s².
2. Record the force of limiting friction (F) directly from the spring balance reading at the instant the block begins to move.
3. Calculate the coefficient of friction (μ) for each observation:
   \[ \mu = \frac{F}{R} \]
4. Calculate the average value of the coefficient of friction:
   \[ \mu_{avg} = \frac{\mu_1 + \mu_2 + \mu_3 + \mu_4 + \mu_5}{5} \]

For plotting the graph:

1. Plot force of limiting friction (F) along the y-axis.
2. Plot normal reaction (R) along the x-axis.
3. Draw the best fit straight line through the plotted points.
4. The slope of this line gives the coefficient of friction (μ).

1. The force of limiting friction (F) is directly proportional to the normal reaction (R), as verified by the linear relationship in the graph.
2. The coefficient of friction (μ) between the wooden block and the horizontal surface is _____ (from the average of calculated values).
3. The slope of the F vs R graph is _____, which represents the coefficient of friction.

1. The horizontal surface should be clean, dry, and free from dust and oil.
2. The wooden block should be placed gently on the surface without any initial motion.
3. The spring balance should be pulled horizontally and parallel to the surface.
4. The force should be applied gradually and smoothly to determine the exact point of motion.
5. The pulley used should be frictionless or have minimal friction.
6. Readings should be taken at the instant the block just begins to move, not after it has started moving.
7. The wooden block should not tilt while being pulled.
8. Weights should be placed centrally on top of the block to ensure uniform distribution of normal reaction.

1. Friction in the pulley may affect the measured force.
2. Non-uniformity of the surface can lead to inconsistent friction values.
3. Jerky application of force might lead to inaccurate readings.
4. Improper alignment of the thread with the horizontal surface.
5. Human error in reading the spring balance at the exact moment of motion.
6. Variation in environmental factors like temperature and humidity can affect friction.
7. Wear and tear of the wooden block's surface during repeated trials.
8. Possible presence of impurities on the surfaces in contact.

1. Q: What is the difference between static friction and kinetic friction?
   A: Static friction acts between surfaces at rest relative to each other, while kinetic friction acts between surfaces in relative motion. Static friction is generally greater than kinetic friction.
2. Q: Why is the coefficient of friction dimensionless?
   A: The coefficient of friction is dimensionless because it is the ratio of two forces (friction force and normal force) having the same dimensions.
3. Q: How does the area of contact affect the force of friction?
   A: According to the laws of solid friction, the force of friction is independent of the apparent area of contact between the surfaces.
4. Q: What would happen to the coefficient of friction if the surface is lubricated?
   A: Lubrication reduces the direct contact between surfaces, which decreases the coefficient of friction.
5. Q: Why is the graph between limiting friction and normal reaction expected to be a straight line?
   A: The graph is expected to be a straight line because according to the law of friction, limiting friction is directly proportional to the normal reaction (F = μR).
6. Q: What factors can affect the value of the coefficient of friction?
   A: The coefficient of friction depends on the nature of surfaces in contact, surface roughness, temperature, presence of contaminants or lubricants, and environmental conditions.
7. Q: Why does the block move with constant velocity once it starts moving (assuming constant pulling force)?
   A: Once the block starts moving, static friction is replaced by kinetic friction, which is typically less than static friction. If the applied force equals the kinetic friction force, the net force becomes zero, resulting in constant velocity according to Newton's first law.
8. Q: How would the results change if the experiment was conducted on an inclined plane?
   A: On an inclined plane, the normal reaction would decrease (R = mg·cos(θ)), and there would be a component of weight acting down the plane (mg·sin(θ)). The coefficient of friction could still be determined, but the experimental setup and calculations would be different.