25 N effort is required to slide the barrel of 1 kN. The coefficient of friction is
0.025
Calculating Coefficient of Friction for a Sliding Barrel
The problem asks us to determine the coefficient of friction when an effort of 25 N is required to slide a barrel weighing 1 kN. Understanding the relationship between friction force, normal force, and the coefficient of friction is key to solving this problem.
Friction Force and Normal Force Principles
When an object is sliding or about to slide over a surface, the force opposing its motion is called the friction force. The friction force is directly proportional to the normal force pressing the object against the surface. The constant of proportionality is known as the coefficient of friction.
- Effort (Friction Force): This is the force required to initiate or maintain the sliding motion of the barrel. In this problem, the effort given is 25 N. This represents the force that overcomes the static friction to start sliding, or the kinetic friction to continue sliding.
- Weight of the Barrel (Normal Force): For an object resting on a horizontal surface, its weight acts vertically downwards. The surface exerts an equal and opposite force, called the normal force, vertically upwards. Therefore, the weight of the barrel represents the normal force acting on the surface. The weight is given as 1 kN.
Unit Conversion for Barrel's Weight
Before proceeding with the calculation, it is essential to ensure all forces are in consistent units. The effort is given in Newtons (N), but the weight of the barrel is in kiloNewtons (kN). We need to convert kiloNewtons to Newtons to maintain consistency in our calculations.
We know that the standard conversion factor is:
$$1 \text{ kN} = 1000 \text{ N}$$Therefore, the weight of the barrel, which acts as the Normal Force (\(N\)) in this scenario, is:
$$N = 1 \text{ kN} = 1 \times 1000 \text{ N} = 1000 \text{ N}$$Formula for Coefficient of Friction
The fundamental relationship that connects friction force, coefficient of friction, and normal force is given by the formula:
$$F_f = \mu \times N$$Where:
- \(F_f\) is the friction force (the effort required to slide the barrel).
- \(\mu\) (mu) is the coefficient of friction (the value we need to find).
- \(N\) is the normal force (the weight of the barrel).
To find the coefficient of friction (\(\mu\)), we can rearrange this formula as:
$$\mu = \frac{F_f}{N}$$Step-by-Step Calculation of Coefficient of Friction
Now, let's substitute the given values into the rearranged formula:
- Friction Force (\(F_f\)) = 25 N
- Normal Force (\(N\)) = 1000 N (after conversion)
Substituting these values into the formula for \(\mu\):
$$\mu = \frac{25 \text{ N}}{1000 \text{ N}}$$Performing the division:
$$\mu = 0.025$$The coefficient of friction is a dimensionless quantity because it is a ratio of two forces, and thus their units cancel out.
| Parameter | Value |
|---|---|
| Effort (Friction Force, \(F_f\)) | 25 N |
| Weight of Barrel (Normal Force, \(N\)) | 1 kN \(=\) 1000 N |
| Calculated Coefficient of Friction (\(\mu\)) | 0.025 |
Conclusion on Coefficient of Friction for Barrel
The calculated coefficient of friction for sliding the barrel is 0.025. This value represents the interaction between the barrel's surface and the surface it is sliding on. A lower coefficient of friction indicates that less force is required to overcome the frictional resistance between the two surfaces.
Important Questions from Friction
The maximum static frictional force that an object experiences just before it begins to slide over a surface is commonly referred to as the:
Coefficient of friction depends upon
Limiting force of friction is the
Coulomb friction is the friction between
The minimum angle made by an inclined plane with the horizontal such that an object placed on the inclined surface just begins to slide is called-
