Motion on a Horizontal Rough Surface: Comprehensive NEET Physics Notes

1. Motion on a Horizontal Rough Surface

When a body moves on a horizontal surface, the motion is influenced by various forces. A rough surface introduces friction, which opposes the motion of the body. Understanding this interaction is essential for solving problems related to mechanics, especially in NEET physics.

1.1 Forces Acting on a Body on a Rough Surface

When a body is placed on a horizontal rough surface, the primary forces acting on it include:

1. Gravitational Force (Weight): This force, $mg$, acts vertically downwards where $m$ is the mass of the body and $g$ is the acceleration due to gravity.
2. Normal Reaction (N): This force acts perpendicular to the surface and balances the weight of the body in the vertical direction. For a horizontal surface, the normal force is given by $N=mg$.
3. Applied Force (F): This is the external force applied to the body, attempting to move it in a horizontal direction.
4. Frictional Force (f): A resistive force that acts opposite to the direction of the applied force. Friction is proportional to the normal force and can be static or kinetic depending on whether the body is at rest or in motion.
5. • Static Friction ($f_s$): This force resists the initiation of motion and adjusts up to a maximum value ($f_{s_{\text{max}}}$) given by: $f_{s_{\text{max}}}={\mu }_{s}N={\mu }_{s}mg$ where ${\mu }_s$ is the coefficient of static friction.
   • Kinetic Friction ($f_k$): Once the body starts moving, kinetic friction opposes its motion and is given by: $f_k={\mu }_{k}N={\mu }_{k}mg$ where ${\mu }_k$ is the coefficient of kinetic friction, and typically ${\mu }_k<{\mu }_s$.

1.2 Condition for Motion

For a body to move on a rough horizontal surface, the applied force must overcome the maximum static friction. This condition is expressed as: $F>f_{s_{\text{max}}}={\mu }_{s}mg$

Once the applied force exceeds this threshold, the body begins to move, and kinetic friction takes over. The motion is then governed by Newton’s second law: $F_{\text{net}}=F-f_k=ma$ where $a$ is the acceleration of the body, and $m$ is its mass.

NEET Tip: Always remember that static friction adjusts to the applied force until it reaches its maximum value. Only when the applied force exceeds $f_{s_{\text{max}}}$ does the body begin to move, after which kinetic friction comes into play.

1.3 Work Done Against Friction

When a body moves on a rough surface, work must be done to overcome friction. The work done against friction is given by: $W=f_k\cdot d={\mu }_{k}mg\cdot d$ where $d$is the displacement of the body along the surface.

Real-life Application: Friction is crucial in daily life, such as when walking. Without friction between your feet and the ground, you would not be able to move forward.

1.4 Acceleration and Net Force

When a body moves on a rough surface with an applied force $F$, the net force responsible for acceleration is: $F_{\text{net}}=F-{\mu }_{k}mg$

According to Newton's second law, the acceleration of the body is: $a=\frac{F-{\mu }_{k}mg}{m}$

This equation shows that the greater the friction (higher ${\mu }_k$), the lower the acceleration for the same applied force.

NEET Problem-Solving Strategy: Always draw a free-body diagram to identify all the forces acting on the object. Break the forces into components, if necessary, and apply Newton's second law to solve for acceleration or other unknowns.

1.5 Energy Dissipation Due to Friction

When a body moves on a rough surface, part of its kinetic energy is converted into heat due to the work done by friction. The loss of kinetic energy, which corresponds to the work done by friction, is: $\Delta K=-f_k\cdot d=-{\mu }_{k}mg\cdot d$

Thus, friction leads to energy dissipation, and over time, the body will eventually come to rest unless continuous force is applied.

NEET Tip: In NEET, questions on friction often involve calculating how far a body moves before stopping due to friction. Be sure to understand the relationship between friction, energy loss, and motion.

1.6 Visual Aids

To better understand the forces involved, below are key diagrams that should be referenced:

• Free-Body Diagram: Depicts forces such as the applied force, friction, and the normal reaction on the body.
• Force Diagrams: Illustrate how static and kinetic friction act at different stages of motion.

Quick Recap

• Friction on a horizontal surface can be static or kinetic depending on whether the body is moving or not.
• The normal force is equal to mg for a horizontal surface.
• The net force on a moving body is given by $F_{\text{net}}=F-{\mu }_{k}mg$, determining its acceleration.
• Work done against friction results in energy dissipation as heat.
• Use Newton’s second law and free-body diagrams for problem-solving.

NEET Exam Strategy

• Focus on identifying all forces acting on the body, especially friction.
• Know how to calculate the limiting force of static friction ($f_{s_{\text{max}}}$) to determine whether the body will start moving.
• When the body moves, calculate acceleration by subtracting kinetic friction from the applied force.
• Remember that energy dissipation due to friction plays a key role in how far an object can travel on rough surfaces.
• Use proper units and always verify calculations for forces, especially when working with coefficients of friction.

Practice Questions

1. A 10 kg box is placed on a rough horizontal surface with a coefficient of static friction ${\mu }_s=0.4$ and kinetic friction ${\mu }_k=0.3$. What is the minimum force required to start moving the box?
2. If the box in question 1 starts moving, calculate the acceleration of the box when a force of 50 N is applied.
3. A body of mass 5 kg is pushed with a force of 30 N on a rough surface with ${\mu }_k=0.2$. What is the distance covered by the body before coming to rest if the applied force is removed after 10 seconds?
4. A 2 kg block slides on a rough surface with a coefficient of kinetic friction ${\mu }_k=0.1$. If the block moves 5 meters under an applied force of 10 N, find the work done against friction.
5. Calculate the velocity of a body after 5 seconds if a 20 N force is applied to a 4 kg object on a surface with ${\mu }_k=0.15$.

Supplementary Features

• Glossary:
• • Static Friction ($f_s$): The force that prevents motion.
  • Kinetic Friction ($f_k$): The force that opposes motion when an object is moving.
  • Normal Force (N): The force perpendicular to the surface supporting the weight of the object.
  • Coefficient of Friction ($\mu$): A constant that represents the ratio of the frictional force to the normal force.
• Quick Reference Guide:
• • Work done against friction: $W=f_k\cdot d$
  • Net force: $F_{\text{net}}=F-{\mu }_{k}mg$
• NEET Problem-Solving Tip: Always ensure all forces are accounted for in free-body diagrams, including normal force and friction. Understand the transition between static and kinetic friction to avoid common pitfalls in NEET questions.