A block of mass 20 Kg is placed on a horizontal surface. Co-efficient of static friction and coefficient of kinematic friction between the block and surface are 0.5 and 0.4 respectively. What is the minimum force required to be applied on the block in horizontal direction so that the block just starts to move. Consider g = 10 m/sec2.
100 N
Block Friction Problem: Understanding Motion Initiation
This problem asks us to determine the minimum horizontal force required to make a block of mass 20 kg just begin to move on a horizontal surface. This scenario specifically involves the concept of static friction, which is the force that opposes the initiation of motion between two surfaces in contact.
Friction Concepts Explained
When a block is placed on a surface, several forces act upon it. The key forces relevant to this problem are:
- Weight (\(W\)): The force exerted by gravity on the block, acting vertically downwards. It is calculated as \(W = mg\), where \(m\) is the mass and \(g\) is the acceleration due to gravity.
- Normal Force (\(N\)): The force exerted by the surface on the block, acting perpendicularly upwards. On a horizontal surface, the normal force is equal in magnitude to the weight of the block.
- Static Friction Force (\(f_s\)): This force opposes the tendency of motion. It acts parallel to the surface and adjusts its magnitude up to a maximum value to prevent the block from moving. The maximum static friction force is given by \(f_{s,max} = \mu_s N\), where \(\mu_s\) is the coefficient of static friction.
- Kinematic (or Kinetic) Friction Force (\(f_k\)): This force opposes the motion of the block once it is already moving. It is given by \(f_k = \mu_k N\), where \(\mu_k\) is the coefficient of kinematic friction.
To make the block just start to move, the applied horizontal force must be equal to or slightly greater than the maximum static friction force. The coefficient of kinematic friction is relevant only after the block has started moving and is therefore not used in this specific calculation.
Given Block Data
Let's list the values provided in the question:
- Mass of the block, \(m = 20 \text{ Kg}\)
- Coefficient of static friction, \(\mu_s = 0.5\)
- Coefficient of kinematic friction, \(\mu_k = 0.4\)
- Acceleration due to gravity, \(g = 10 \text{ m/sec}^2\)
Normal Force Calculation
First, we need to calculate the normal force (\(N\)) acting on the block. Since the block is on a horizontal surface, the normal force is equal to its weight:
$$N = W = mg$$
Substitute the given values:
$$N = (20 \text{ Kg})(10 \text{ m/sec}^2)$$
$$N = 200 \text{ N}$$
So, the normal force acting on the 20 kg block is 200 N.
Static Friction Force Calculation
Next, we calculate the maximum static friction force (\(f_{s,max}\)) that needs to be overcome to initiate motion. This is determined by the coefficient of static friction and the normal force:
$$f_{s,max} = \mu_s N$$
Substitute the values of \(\mu_s\) and \(N\):
$$f_{s,max} = (0.5)(200 \text{ N})$$
$$f_{s,max} = 100 \text{ N}$$
Minimum Force Required to Start Motion
The minimum horizontal force required to make the block just start to move is equal to the maximum static friction force. If the applied force is less than this value, the block will remain stationary. If the applied force is equal to or slightly greater than this value, the block will begin to accelerate.
Therefore, the minimum force required is:
$$\text{Minimum Force} = f_{s,max} = 100 \text{ N}$$
Summary of Forces
| Parameter | Symbol | Value |
|---|---|---|
| Mass of block | \(m\) | 20 Kg |
| Acceleration due to gravity | \(g\) | 10 m/sec\(^2\) |
| Coefficient of static friction | \(\mu_s\) | 0.5 |
| Coefficient of kinematic friction | \(\mu_k\) | 0.4 |
| Normal Force (Weight) | \(N\) | 200 N |
| Maximum Static Friction Force | \(f_{s,max}\) | 100 N |
| Kinematic Friction Force (for reference) | \(f_k\) | 80 N |
The minimum force required to be applied on the block in the horizontal direction so that the block just starts to move is 100 N.
Important Questions from Friction
A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll the wheel along the rail is:
Which of the following option is CORRECT about the methods used to reduce the friction?
Which of the following is NOT a law of static friction?
If we push the break of car then car will begin to slide when:
An elephant is stopped by a rope wound twice around the rough trunk of a tree. If the elephant exerts a pull of 1000 kgf, the minimum force required to stop the elephant is_________. (Coefficient of friction between the rope and the tree is 0.3)
