# Important differences between Force and Momentum

Force

The Driving Factor of Motion

Force is a fundamental concept in physics that describes the interaction between objects and the ability to cause changes in their motion or shape. It plays a central role in understanding the dynamics of physical systems.

Force can be defined as a push or pull that acts on an object, changing its velocity, direction, or shape. It is a vector quantity, meaning it has both magnitude and direction. Force is typically measured in units of Newtons (N) and is denoted by the symbol “F.”

Types of Forces:

There are several types of forces that can act on objects. Some of the common types of forces include:

Contact Forces:

• Normal Force: The normal force acts perpendicular to the surface of contact between two objects and prevents them from passing through each other.
• Frictional Force: Frictional force opposes the motion of an object as it moves across a surface.

Gravity:

Gravitational Force: Gravitational force is the force of attraction between two objects due to their masses. It is responsible for the weight of objects and is always directed toward the center of the Earth.

Applied Forces:

Applied Force: An applied force is a force exerted on an object by a person or another object through direct contact.

Non-Contact Forces:

• Magnetic Force: Magnetic force is exerted by magnets or magnetic fields and can attract or repel objects with magnetic properties.
• Electric Force: Electric force is exerted by charged objects and can attract or repel other charged objects.

Newton’s Laws of Motion:

Force is closely related to Newton’s laws of motion, which describe the behavior of objects in response to forces. These laws include:

• Newton’s First Law (Law of Inertia): An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same velocity unless acted upon by an external force.
• Newton’s Second Law (Law of Acceleration): The acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass (F = ma).
• Newton’s Third Law (Law of Action-Reaction): For every action, there is an equal and opposite reaction. When one object exerts a force on another, the second object exerts an equal and opposite force on the first object.

Measurement of Force:

Force can be measured using various devices, such as spring scales or force sensors, which quantify the amount of force applied. These devices often utilize Hooke’s Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Applications of Force:

The concept of force finds extensive applications in various fields, such as engineering, mechanics, and even everyday life. It is crucial for understanding the motion of objects, designing structures, calculating the performance of machines, and predicting the behavior of systems subjected to external influences.

Momentum

The Measure of Motion

Momentum is a fundamental concept in physics that quantifies the motion of an object. It provides valuable insights into the behavior of moving objects and is widely used in various fields of science.

Momentum can be defined as the product of an object’s mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. Mathematically, momentum (p) is represented as the product of mass (m) and velocity (v), and it is denoted by the symbol p = mv.

Impulse and Momentum:

Impulse is the change in momentum of an object and is closely related to the concept of force and the time over which it acts. When a force is applied to an object for a certain duration, it changes the object’s momentum. The impulse experienced by an object is equal to the change in momentum, and it is given by the equation J = Δp = FΔt, where F is the force applied and Δt is the time interval over which the force acts.

Conservation of Momentum:

According to the law of conservation of momentum, the total momentum of a closed system remains constant if no external forces act on it. In other words, the total momentum before an event is equal to the total momentum after the event. This principle is derived from Newton’s third law of motion, which states that for every action, there is an equal and opposite reaction.

Momentum in Collisions:

Momentum is particularly useful in the study of collisions between objects. During a collision, the total momentum of the system is conserved, allowing us to analyze the behavior of the objects before and after the collision. There are two types of collisions: elastic and inelastic. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, only momentum is conserved, and some kinetic energy is lost.

Applications of Momentum:

The concept of momentum finds extensive applications in various fields, including physics, engineering, and sports. It helps in analyzing the motion of objects, designing efficient transportation systems, studying particle interactions in high-energy physics, and even in sports like billiards or car racing, where understanding the transfer of momentum is crucial.

Calculation of Momentum:

To calculate momentum, the mass of the object and its velocity must be known. The mass is typically measured in kilograms (kg), and the velocity is measured in meters per second (m/s). By multiplying the mass and velocity, we obtain the momentum of the object.

Important differences between Force and Momentum

 Basis of Comparison Force Momentum Definition Force is a push or pull that can change an object’s motion or shape. Momentum is the product of an object’s mass and velocity. Quantity Type Force is a vector quantity with both magnitude and direction. Momentum is a vector quantity with both magnitude and direction. Cause of Change Force causes changes in an object’s motion or shape. Momentum describes an object’s motion and is a measure of its motion. Measurement Unit Force is measured in Newtons (N). Momentum is measured in kilogram-meter per second (kg·m/s). Relationship to Mass and Acceleration Force is proportional to mass times acceleration (F = ma). Momentum is the product of mass and velocity (p = mv). Conservation Principle Forces can change the total momentum of a system. The total momentum of a closed system is conserved if no external forces act on it (Law of Conservation of Momentum). Collisions Forces are involved in causing changes in momentum during collisions. Momentum is conserved in collisions, allowing analysis of the behavior of objects before and after the collision.

Force and Momentum numeric question with answer

Question:

A car of mass 1000 kg is traveling at a velocity of 20 m/s. It experiences a constant force of 2000 N in the opposite direction. Calculate the change in momentum of the car after 5 seconds.

Solution:

Given:

Mass of the car (m) = 1000 kg

Velocity of the car (v) = 20 m/s

Force acting on the car (F) = -2000 N (opposite direction)

First, let’s calculate the initial momentum of the car using the formula:

Momentum (p) = mass (m) × velocity (v)

Initial momentum (p1) = m × v = 1000 kg × 20 m/s = 20000 kg·m/s

Next, let’s calculate the final velocity of the car using Newton’s second law of motion:

Force (F) = mass (m) × acceleration (a)

Acceleration (a) = F / m = (-2000 N) / 1000 kg = -2 m/s^2 (opposite direction)

Using the equation of motion:

v = u + at

Final velocity (v2) = 20 m/s + (-2 m/s^2) × 5 s = 20 m/s – 10 m/s = 10 m/s

Now, let’s calculate the final momentum of the car using the formula:

Final momentum (p2) = m × v2 = 1000 kg × 10 m/s = 10000 kg·m/s

The change in momentum (Δp) is given by:

Δp = p2 – p1 = 10000 kg·m/s – 20000 kg·m/s = -10000 kg·m/s

The negative sign indicates that the change in momentum is in the opposite direction to the initial momentum.

Therefore, the change in momentum of the car after 5 seconds is -10000 kg·m/s.