Solving Problems in Mechanics: Methods & Approaches, Free Body Diagram, Important Formula, Tips

To begin solving mechanics problems in Physics Class 11, follow these approaches first.

• Identifying the system correctly while reading the question for the numerical. This is the approach to master all mechanics physics chapters.   
• Drawing accurate free-body diagrams (FBDs) before you start solving the problem or jumping into equations. The key is to visualise types of forces, including tension, gravity, and normal force. 
• Applying Newtonian Laws and using the correct kinematic equations, where you should know whether integrating forces, including friction, and tension, is needed or not. That should be backed by core concepts such as momentum conservation or similar.

Let's follow the steps to solve problems in mechanics. By the end of it, you will be sorted to get answers quickly. 

Step 1: Define the Object or System

Start by identifying the system. It could range from a single block on an inclined plane or two masses in a pulley, and to even particles in a system going through collision. 

Once you are clear on it, try to specify whether the same system is in equilibrium or motion. Here, we can give you an example of a block on an incline.

Now, this block in the system will have three types of forces, including gravity, normal force, and friction.

Step 2: Draw an FBD

Before you apply any formula you learnt from the earlier mechanics physics chapters, draw the free-body diagram.

Doing this will show all forces acting on each object.

We can think of weight ( mg ), normal force ( $N$  ), friction ( $f$ ), and tension ( $T$  ), as from the earlier section of the chapter on the common forces in mechanics.

One common mistake is that you can avoid is by labelling all the different forces correctly.

Step 3: Choose the Right Coordinate System

It's essential to select a coordinate system so that you can easily simplify the calculations. The context is important here. 

• For all inclined planes, align axes along and perpendicular to the incline.
• For circular motion, use radial and tangential directions. 

Step 4: Resolve Forces Along the Axes

Following the above, you should start at breaking down the forces into different components. They must along the axes you choose.

If you are considering a block on an incline angle $\theta )$ then, $W_x=mg\mathrm{s}\mathrm{i}\mathrm{n}\theta ,\mathrm{}{W}_y=mg\mathrm{c}\mathrm{o}\mathrm{s}\theta$

This step is tied to Newton's Second Law. 

Step 5: Apply Newton's Laws to Set Up Equations

The most important part: use Newton's laws to set up the equation

• First Law of Motion: For equilibrium, $\sum \vec{F}=0$ .
• Second Law of Motion: For motion, $\sum \vec{F}=m\vec{a}$ .
• Third Law of Motion: For interacting objects, action-reaction pairs apply. For collisions, use conservation of momentum if external forces are negligible.

Step 6: Solve the Equations for Unknowns

After setting up the equations, you can combine them from the FBDs you drew earlier.

Then you can solve each for the unknowns, including acceleration and tension, or similar.

Remember to use kinematic equations for displacement or time. 

Step 7: Verify the Results

The final step is to verify the results after you have set up the equations and solved for the unknowns.

What you should do then is to check the units. Remember SI Units like N for force, kg for mass, $\mathrm{m}/{\mathrm{s}}^2$ for acceleration.

Also look for physical plausibility, where positive tensions could be there, for instance. 

Before solving problems in mechanics, always remember these equations. 

• Equilibrium: $\sum \vec{F}=0$
• Motion: $\sum \vec{F}=m\vec{a}$
• Momentum: $\sum m_i{\vec{v}}_i=\sum m_i{\vec{v}}_i^{\text{'}}$ (
• Friction: $f_s\le {\mu }_{s}N,f_k={\mu }_{k}N$

Follow the steps above to answer this question, which tests your ability to find the force balance and friction. This type of question is valuable for JEE Main.  

Problem: A 3 kg block on a ${30}^{\circ }$  incline ( ${\mu }_s=0.4$  ) is pushed with a force $F=20\mathrm{N}$  parallel to the incline. Find the acceleration.

Solution:

• Forces: Weight ( $W=mg=3\cdot 9.8=29.4\mathrm{N}$ ), normal force ( $N=mg\mathrm{c}\mathrm{o}\mathrm{s}{30}^{\circ }=$ $29.4\cdot 0.866=25.46\mathrm{N}$  ), friction ( $f_s={\mu }_{s}N=0.4\cdot 25.46=10.18\mathrm{N}$  ).
• Net force down incline: $F_{\text{net}}=F-W\mathrm{s}\mathrm{i}\mathrm{n}{30}^{\circ }-f_s=20-29.4\cdot 0.5-10.18=$ $20-14.7-10.18=-4.88\mathrm{N}$ .
• Since $F_{\text{net}}$ is negative, check if static friction holds: $F=20<14.7+$ $10.18=24.88$ , so the block doesn't move, and acceleration $=0\mathrm{m}/{\mathrm{s}}^2$ .

 

Want more Physics chapter notes for Class 11? Go through these links. 

Units and Measurements Class 11 Notes	Mechanical Properties of Solids Class 11 Notes
Motion in a Straight Line Class 11 Notes	Mechanical Properties of Fluids Class 11 Notes
NCERT Class 11 Notes for Motion in a Plane	Thermal Properties of Matter Class 11 Notes
Laws of Motion Class 11 Notes	Thermodynamics Class 11 Notes
Work, Energy, and Power Class 11 Notes	Kinetic Theory of Gas Class 11 Notes
System of Particles and Rotational Motion Class 11 Notes	Oscillations Class 11 Notes
Gravitation Class 11 Notes	Waves Class 11 Notes

Click on these additional links for Class 11 Science revision notes.

NCERT Class 11 Notes for PCM

NCERT Class 11 Physics Notes

 

Need more NCERT Solutions for Physics Class 11? Or, if you are looking to solve solutions for each chapter, check these. 

Units and Measurements Class 11 NCERT Solutions	Mechanical Properties of Solids Class 11 NCERT Solutions
Motion in a Straight Line Class 11 NCERT Solutions	Mechanical Properties of Fluids Class 11 NCERT Solutions
Motion in a Plane Class 11 NCERT Solutions	Thermal Properties of Matter Class 11 NCERT Solutions
Laws of Motion Class 11 NCERT Solutions	Thermodynamics Class 11 NCERT Solutions
Work, Energy, and Power Class 11 NCERT Solutions	Kinetic Theory Class 11 NCERT Solutions
System of Particles and Rotational Motion Class 11 NCERT Solutions	Oscillations Class 11 NCERT Solutions
Gravitation Class 11 NCERT Solutions	Waves Class 11 NCERT Solutions