Connected Bodies and Apparent Weight: Comprehensive NEET Physics Notes

1. Connected Bodies

1.1 Introduction to Connected Bodies

Connected bodies in mechanics refer to systems where two or more objects are linked through a rope, string, or any connector. The motion of one object directly impacts the motion of the others due to the constraints provided by the connector. This concept is particularly important when solving problems involving pulleys or inclined planes, which are common in NEET exam questions.

1.2 Tension in Strings and Acceleration of Connected Bodies

In systems of connected bodies, the tension in the string plays a crucial role in determining the motion. Newton's second law is applied to each object to find the system's common acceleration. Consider the following typical cases:

1. Two Blocks on a Smooth Horizontal Surface Connected by a String:
2. • When a force $F$ is applied on one block, both blocks move with a common acceleration $a$.
   • The tension in the string transmits the force between the two blocks.
2. Two Bodies Connected by a Pulley System:
3. • When two blocks are connected via a string passing over a pulley, one moves upward as the other moves downward. The tension in the string is constant throughout the system, and the accelerations are interdependent.

Key Equations

For solving connected-body problems, the following equations are used:

• For Block 1:
  $T-m_{1}g=m_{1}a$
• For Block 2:
  $m_{2}g-T=m_{2}a$

Where:

• $T$ represents the tension in the string,
• $m_{1}and{m}_2$ are the masses of the two blocks,
• $a$ is the common acceleration of both blocks.

Solving these equations simultaneously helps determine the system's acceleration and tension.

2. Apparent Weight

2.1 Understanding Apparent Weight

Apparent weight refers to the force exerted by an object on a surface, which may differ from its actual weight depending on the object’s acceleration. Apparent weight changes when an object is in an accelerated frame, such as an elevator, providing important insights for problem-solving.

2.2 Apparent Weight in Elevators

In an elevator, a person's apparent weight changes based on the elevator's motion:

1. Elevator at Rest:
   The apparent weight equals the true weight:
   $W_{\text{apparent}}=mg$
2. Elevator Accelerating Upwards:
   Apparent weight increases due to the additional force from acceleration:
   $W_{\text{apparent}}=m(g+a)$
3. Elevator Accelerating Downwards:
   Apparent weight decreases:
   $W_{\text{apparent}}=m(g-a)$
4. Free Fall:
   During free fall, the apparent weight becomes zero, causing a sensation of weightlessness:
   $W_{\text{apparent}}=0$

Did You Know?
Astronauts in space experience weightlessness due to free fall, where their apparent weight becomes zero.

2.3 Applications of Apparent Weight

Apparent weight is critical in real-life applications, such as:

• Elevators: Designing elevators requires understanding how apparent weight changes to ensure safety.
• Amusement park rides: Roller coasters use apparent weight changes to create thrilling experiences.
• Astronaut training: Simulating weightlessness on Earth helps astronauts prepare for space missions.

Quick Recap

• Connected bodies involve two or more objects linked by a connector, and their motion is interdependent.
• The tension in the string and Newton’s second law are crucial for solving connected-body problems.
• Apparent weight is the normal force felt by an object and can vary when the object is in an accelerated frame, such as in an elevator.

Concept Connection

In Biology, weightlessness experienced in space affects muscle and bone density, showing a direct connection to the concept of apparent weight. In Chemistry, forces between molecules, such as gravitational attraction, can also be related to mechanics concepts like tension and weight.

NEET Problem-Solving Strategy

For connected-body problems:

1. Draw a free-body diagram for each object.
2. Apply Newton’s second law to each object, considering forces like tension and gravity.
3. Solve the equations to find unknowns such as acceleration and tension.

For apparent weight problems:

1. Identify the type of motion (rest, upward, or downward acceleration).
2. Use the appropriate formula for apparent weight based on the scenario.

Practice Questions

1. Two blocks of masses 3 kg and 5 kg are connected by a string passing over a pulley. One block is on a smooth horizontal surface, and the other is hanging. Find the acceleration and tension.
2. A person in an elevator observes that their weight appears to be 20% greater than their actual weight. Determine the acceleration of the elevator.
3. A 10 kg block on an inclined plane is connected to a 5 kg block by a string over a pulley. Calculate the acceleration and tension in the string.
4. What is the reading on a weighing scale for a 60 kg person in an elevator accelerating upwards at 2 m/s²?
5. A 50 kg object in an elevator experiences downward acceleration at 4 m/s². What is its apparent weight?

Solutions

1. Acceleration:
   $a=\frac{m_{2}g}{m_1+m_2}=\frac{5\times 9.8}{3+5}=6.13{\text{m/s}}^2$
   Tension:
   $T=m_{1}a=3\times 6.13=18.39\text{N}$
2. Acceleration:
   The apparent weight is 20% more:
   $1.2mg=m(g+a)⟹a=0.2g=1.96{\text{m/s}}^2$
3. Acceleration:
   $a=\frac{(m_2-m_1\sin 30^{\circ })g}{m_1+m_2}$
   Tension:
   $T=m_1(g-a)$
4. Apparent Weight:
   $W_{\text{apparent}}=m(g+a)=60\times (9.8+2)=708\text{N}$
5. Apparent Weight:
   $W_{\text{apparent}}=m(g-a)=50\times (9.8-4)=290\text{N}$

Areas for Improvement:

1. Clarify Concepts: Pay close attention to the difference between tension, actual weight, and apparent weight. These terms are often confused in exam scenarios.
2. Practice Free-body Diagrams: Many problems involving connected bodies require detailed free-body diagrams. Be sure to practice drawing and interpreting these diagrams accurately.
3. Work on Timing: Connected-body problems can take time to solve. Practice under timed conditions to improve speed and accuracy.

Final Recommendations for Increasing the Score:

1. Solve More Practice Problems: Focus on a variety of connected-body and apparent weight problems from past NEET exams.
2. Use Mnemonics and Visuals: Employ mnemonics to remember key formulas and draw visual aids such as free-body diagrams to enhance understanding.
3. Revise Key Formulas Regularly: Regularly revise key formulas related to Newton’s laws, tension, and apparent weight to ensure they are well memorized before the exam.