Chapter 6: How Forces Affect Motion
6.1 The Concept of Force
6.1.1 What is Force?
- Force: A push or pull that can make an object move from rest, change its speed or direction of motion, or change its shape.
- Vector Nature: Force is a physical quantity for which we need to specify both magnitude and direction along with its unit.
- SI Unit of Force: The SI unit of force is the newton (symbol: N).
6.1.2 Measuring Force
- Spring Balance: A device used to measure the magnitude of a force by stretching an internal spring.
- Weight: The gravitational force with which the Earth pulls an object downward.
6.2 Balanced and Unbalanced Forces
6.2.1 Force Types
- Balanced Forces: Two forces acting on an object that are equal in magnitude and opposite in direction, resulting in no change in the state of rest or motion.
- Unbalanced Forces: Forces that are unequal in magnitude or not opposite, producing a non-zero net force that causes acceleration.
- Net Force: The single combined force representing the vector sum of all individual forces acting on an object.
6.3 The Force of Friction
6.3.1 Mechanics of Friction
- Force of Friction: An opposing force that arises between the contact surfaces of two objects and acts in a direction opposite to the relative motion or applied force.
- Normal Force: The perpendicular upward force exerted by a surface supporting an object, balancing its downward gravitational pull.
6.4 Newton’s First Law of Motion
6.4.1 The Law of Inertia
- Newton's First Law: An object at rest remains at rest, and an object in motion continues to move with a constant velocity, unless a net force acts upon it.
- Inertia: The inherent tendency of objects to resist any change in their state of rest or uniform motion.
6.5 Newton’s Second Law of Motion
6.5.1 Force, Mass, and Acceleration
- Newton's Second Law: When a net force acts on an object, the object accelerates in the direction of the net force with a magnitude directly proportional to the force and inversely proportional to its mass ($F = ma$).
- Acceleration due to Gravity: Denoted by g, it represents the gravitational acceleration (approximately $9.8 \text{ m s}^{-2}$ near Earth's surface).
- Momentum: Defined as the product of an object's mass and its velocity ($p = mv$).
6.6 Newton’s Third Law of Motion
6.6.1 Action and Reaction Pairs
- Newton's Third Law: Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal and opposite force on the first object.
- Action-Reaction Pairs: Equal and opposite forces that act on two different interacting objects, meaning they do not cancel each other out.
6.7 Forces Acting on a System of Objects
6.7.1 System Dynamics
- System of Objects: Connective bodies grouped together to simplify analysis by treating internal forces as cancelling pairs.
- Internal Forces: Forces acting strictly between components of a system, such as string tension, which do not accelerate the system as a whole.
- External Forces: Net forces acting on the system from outside sources that govern the overall acceleration of the combined mass.