Laws of Motion (Dynamics): NMAT Physics Review

The Laws of Motion form the foundation of dynamics, a major topic in NMAT Physics. These laws, formulated by Sir Isaac Newton, explain how and why objects move under the influence of forces. A solid understanding of dynamics is essential for solving NMAT problems involving acceleration, forces, equilibrium, friction, circular motion, and applications in real-life situations.

In the NMAT, questions on the Laws of Motion test not only memorization but also conceptual understanding and problem-solving skills. This review provides a comprehensive and exam-oriented discussion of Newton’s Laws, free-body diagrams, common forces, and key applications.

Introduction to Dynamics

Dynamics is the branch of mechanics that deals with the motion of objects and the forces that cause or change that motion. Unlike kinematics, which describes motion without considering forces, dynamics explains motion by analyzing the interaction between forces and mass.

In NMAT Physics, dynamics problems typically involve:

• Identifying forces acting on an object
• Applying Newton’s Laws of Motion
• Solving equations involving force, mass, and acceleration
• Understanding equilibrium and non-equilibrium situations

Newton’s First Law of Motion (Law of Inertia)

Newton’s First Law states:

An object remains at rest or continues to move with constant velocity in a straight line unless acted upon by a net external force.

This law introduces the concept of inertia, which is the resistance of an object to changes in its state of motion. Objects with larger mass have greater inertia and require larger forces to change their motion.

Key Concepts in the First Law

The First Law applies when the net force is zero. This does not mean that no forces act on the object, but rather that all forces balance each other.

• If net force = 0 → object is in equilibrium
• Object may be at rest or moving with constant velocity

For NMAT problems, recognizing equilibrium conditions is crucial, especially in questions involving objects at rest or moving uniformly.

Examples of Newton’s First Law

Common real-life examples include:

• A book resting on a table remains at rest because gravitational force is balanced by the normal force
• A passenger lurches forward when a bus suddenly stops due to inertia
• An object sliding on a frictionless surface continues moving indefinitely

In NMAT questions, inertia-related concepts are often tested through conceptual or situational problems.

Newton’s Second Law of Motion

Newton’s Second Law describes how force affects motion. It states:

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Mathematically, this is expressed as:

F = ma

where:

• F = net force (in newtons)
• m = mass (in kilograms)
• a = acceleration (in m/s²)

Understanding Force, Mass, and Acceleration

The Second Law shows that:

• Increasing force increases acceleration
• Increasing mass decreases acceleration for the same force

This relationship is central to solving NMAT numerical problems. Always ensure that units are consistent when applying the formula.

Units of Force

The SI unit of force is the newton (N).

One newton is defined as the force required to accelerate a 1 kg mass by 1 m/s².

In equations, forces must be expressed in newtons to avoid calculation errors.

Newton’s Third Law of Motion

Newton’s Third Law states:

For every action, there is an equal and opposite reaction.

This law emphasizes that forces always occur in pairs. These force pairs act on different objects and do not cancel each other.

Action-Reaction Force Pairs

Key points to remember:

• Action and reaction forces are equal in magnitude
• They act in opposite directions
• They act on different objects

NMAT questions often test whether students mistakenly assume action-reaction forces cancel each other. Since they act on different bodies, they cannot cancel.

Examples of Newton’s Third Law

• A person walking pushes the ground backward; the ground pushes the person forward
• A rocket expels gases downward; gases push the rocket upward
• A swimmer pushes water backward; water pushes the swimmer forward

Free-Body Diagrams (FBD)

A free-body diagram is a visual representation showing all the forces acting on an object.

Drawing accurate FBDs is a critical skill for NMAT Physics, as most dynamics problems rely on correctly identifying forces.

Steps to Draw a Free-Body Diagram

1. Isolate the object of interest
2. Identify all external forces acting on the object
3. Draw arrows representing each force with proper direction
4. Label all forces clearly

Common mistakes include missing forces or adding forces that do not act directly on the object.

Common Forces in Dynamics

Understanding common forces is essential for NMAT success.

Gravitational Force (Weight)

The gravitational force acting on an object near Earth’s surface is called its weight.

Weight is given by:

W = mg

where g ≈ 9.8 m/s².

Normal Force

The normal force is the support force exerted by a surface perpendicular to the surface of contact.

It does not always equal the weight of the object, especially on inclined planes or when additional forces are applied.

Frictional Force

Friction opposes relative motion between two surfaces in contact.

Types of friction:

• Static friction
• Kinetic (sliding) friction

Frictional force is given by:

f = μN

where μ is the coefficient of friction and N is the normal force.

Tension Force

Tension is the force transmitted through a string, rope, or cable when it is pulled tight.

In ideal problems, strings are assumed to be massless and inextensible, and pulleys are frictionless.

Equilibrium and Net Force

An object is in equilibrium when the net force acting on it is zero.

• Static equilibrium: object at rest
• Dynamic equilibrium: object moving with constant velocity

For equilibrium problems, the sum of forces in all directions must be zero.

Dynamics on Inclined Planes

Inclined plane problems are common in NMAT Physics.

For an object on an inclined plane:

• Weight is resolved into parallel and perpendicular components
• Parallel component causes motion
• Normal force balances the perpendicular component

Using trigonometric relationships is essential when analyzing forces on slopes.

Applications of Newton’s Laws

Newton’s Laws are applied in many NMAT-style problems, including:

• Objects connected by strings
• Elevators and apparent weight
• Motion under constant force
• Objects with friction

Practicing a wide variety of problems strengthens conceptual understanding and speed.

Common NMAT Mistakes in Dynamics

• Confusing mass and weight
• Ignoring action-reaction force pairs
• Incorrect free-body diagrams
• Forgetting to resolve forces into components
• Using incorrect sign conventions

NMAT Exam Tips for Laws of Motion

To perform well in NMAT dynamics questions:

• Master free-body diagrams
• Memorize key formulas but focus on concepts
• Practice time-efficient problem-solving
• Check units and directions carefully

Conclusion

The Laws of Motion are the backbone of NMAT Physics and provide the tools needed to analyze real-world motion. By understanding Newton’s three laws, identifying forces correctly, and applying equations logically, you can confidently solve dynamics problems in the exam.

Consistent practice, strong conceptual clarity, and careful analysis will ensure success in the Laws of Motion section of the NMAT Physics exam.

Problem Set: Laws of Motion (Dynamics)

Problem 1

A 5 kg cart is pushed horizontally with a net force of 20 N.
Find its acceleration.

Problem 2

A 2.5 kg object accelerates at 6 m/s².
What net force is required?

Problem 3

A box slides on a frictionless floor at constant velocity.
Which statement is correct?

• A. No forces act on the box.
• B. Net force is zero.
• C. Acceleration is nonzero.
• D. Force is proportional to velocity.

Problem 4

Find the weight of a 12 kg object near Earth’s surface.

Problem 5

A 10 kg box rests on a horizontal surface.
What is the normal force acting on it?

Problem 6

An 8 kg block slides on a horizontal surface.
The coefficient of kinetic friction is 0.25.
Find the friction force.

Problem 7

A 6 kg box is pulled horizontally by a 30 N force.
The coefficient of kinetic friction is 0.20.
Find the acceleration.

Problem 8

A box remains at rest while you push it with a small force.
Which statement about static friction is correct?

• A. Static friction is always equal to μ_sN.
• B. Static friction adjusts to match the applied force up to a maximum.
• C. Static friction acts in the direction of motion.
• D. Static friction decreases when the applied force increases.

Problem 9

A 3 kg mass hangs at rest from a light rope.
What is the tension in the rope?

Problem 10

Two blocks of masses 2 kg and 3 kg are in contact on a frictionless surface.
A force of 25 N is applied to the 2 kg block.
Find the acceleration of the system.

Problem 11

Using the setup in Problem 10, find the contact force exerted on the 3 kg block.

Problem 12

A 10 kg block rests on a frictionless 30° incline.
Find the component of its weight parallel to the incline.

Problem 13

For the block in Problem 12, find its acceleration down the incline.

Problem 14

A 5 kg block slides down a 37° incline with coefficient of kinetic friction 0.20.
Find the acceleration.

Problem 15

A 60 kg person stands on a scale in an elevator accelerating upward at 2.0 m/s².
What is the scale reading?

Problem 16

The same elevator accelerates downward at 1.5 m/s².
What is the scale reading now?

Problem 17

A book rests on a table.
Which pair of forces is an action–reaction pair?

• A. Weight of book and normal force on book
• B. Normal force on book and normal force on table
• C. Force of book on table and force of table on book
• D. Weight of book and weight of table

Problem 18

A car moves at constant speed in a straight line on a level road.
What can be said about the net force on the car?

Problem 19

Two masses 4 kg and 2 kg are connected by a light rope over a frictionless pulley.
Find the acceleration and the tension.

Problem 20

A 15 kg crate rests on a horizontal floor.
The coefficient of static friction is 0.40.
Find the minimum force needed to start the motion.

Answer Keys

Problem 1 Answer

a = F/m = 20/5 = 4.0 m/s²

Problem 2 Answer

F = ma = 2.5 × 6 = 15 N

Problem 3 Answer

B. Constant velocity implies zero net force.

Problem 4 Answer

W = mg = 12 × 9.8 = 117.6 N

Problem 5 Answer

N = mg = 10 × 9.8 = 98 N

Problem 6 Answer

f = μN = 0.25 × (8 × 9.8) = 19.6 N

Problem 7 Answer

a = (30 − 11.76)/6 = 3.04 m/s²

Problem 8 Answer

B

Problem 9 Answer

T = mg = 3 × 9.8 = 29.4 N

Problem 10 Answer

a = 25/(2+3) = 5.0 m/s²

Problem 11 Answer

F = ma = 3 × 5 = 15 N

Problem 12 Answer

W_∥ = mg sin30° = 49 N

Problem 13 Answer

a = g sin30° = 4.9 m/s²

Problem 14 Answer

a = 4.31 m/s²

Problem 15 Answer

N = m(g + a) = 708 N

Problem 16 Answer

N = m(g − a) = 498 N

Problem 17 Answer

C

Problem 18 Answer

Net force is zero.

Problem 19 Answer

a = 3.27 m/s², T = 26.1 N

Problem 20 Answer

F = μ_smg = 58.8 N

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