Chapter 5- Force and Motion I

INTRODUCTION TO PHYSICS (5)

• While physics is a study of motion, it also includes the ways motion is produced or affected.
• In general, physics is a study of what can cause an object to accelerate.
• The cause of the change in an object’s motion is force, which can be simply described as a push or a pull, but affects the velocity of an object.

NEWTONIAN MECHANICS

• The relation between force and motion is called Newtonian Mechanics, named after Isaac Newton, the scientist who identified this relationship for the first time.
• Newtonian mechanics has 3 main laws.
• While Newtonian mechanics apply to most situations, sometimes they have to be replaced with another study.
• When the speed of an object becomes extremely large (near the speed of light), Newtonian mechanics is replaced with Einstein’s theory of relativity.
• When the size of the object becomes extremely small (near the atom’s size), Newtonian mechanics is replaced with quantum physics.

NEWTON’S FIRST LAW

• Newton’s first law states that if no force acts on a body, the body’s velocity cannot change; that is, the body cannot accelerate.
• This means that if an object is at rest, it will stay at rest. If the object is moving, it will keep moving at the same speed and in the same direction, i.e. at constant velocity.
• If a puck is slid over a slippery surface, it continues to move for a long time and covers a long distance. If we imagine that puck on a frictionless surface, it would hardly slow unless a force is applied to stop it.
• This validates Newton’s first law of motion.

FORCE

• UNIT: The unit of force can be stated in terms of the acceleration a force would give to the standard kilogram. That is, if a force causes an object of mass 1 kg to accelerate at a rate of 1m/s^2, the force is said to be of 1 Newton (N).
• Newton’s second law (later discussed) will enable us to derive the base units of Newton as kg.m/s^2.
• VECTORS: Since force has both, a unit and direction, it is a vector quantity. Therefore, the net force applied to an object can be determined by the resultant vectors (by adding them together.)
• A single force that has the same magnitude and direction as the calculated net force would then have the same effect as all the individual forces. This phenomenon is called the principle of superposition for forces.
• Using the ideas above, the first law of motion can be more clearly stated in terms of net force as: If no net force acts on a body, the body’s velocity cannot change; that is, the body cannot accelerate.
• If there are multiple forces on a body but they cancel each other out to make the net force zero, the body cannot accelerate, i.e. every body with a constant acceleration has a net force of zero.

INERTIAL REFERENCE FRAMES

• Since Newtonian Mechanics is not true for all reference frames, the reference frames in which Newton’s laws hold are called inertial reference frames, or simply inertial frames.
• Commonly, we assume that ground is an inertial frame, although it might always not be in real life, e.g. when a vehicle is accelerating relative to the ground.

MASS

• According to common knowledge, it is true that an object with a larger mass accelerates less.
• Scientifically, we can say that acceleration due to force applied is inversely proportional to the mass of an object.
• Mass is an intrinsic characteristic of a body. While density, weight and size are sometimes confused with mass, in reality, mass can only be described as the characteristic of a body that relates a force on the body to the resulting acceleration.

NEWTON’S SECOND LAW

• The above relationship between mass and force can be summarised as the Newton’s second law of motion which states that the net force on a body is equal to the product of the body’s mass and its acceleration, i.e. F= ma.
• It is important to ensure that the force F in the equation above is the net force (the sum of all forces on the object). The type of body should also be considered.
• It is also to be ensured that the net force is component along an axis to the acceleration along that same axis, and is completely unrelated to other axes.
• Simply, the acceleration component along a given axis is caused only by the sum of the force components along that same axis, and not by force components along any other axis.

FORCES IN EQUILIBRIUM

• When a body is at rest or traveling at a constant velocity, the forces acting on it cancel each other out. In this case, the forces and the body are both said to be in equilibrium.
• It is important to note that the term ‘cancel’ does not mean that forces stop existing. It means that the forces cannot affect the motion of the body anymore.
• To make it simple to use Newton’s second law, we draw a free-body diagram in which the body for which we have to calculate forces is the only represented body (usually with a dot). A coordinate system is also included.
• A system is a group of one or more bodies.
• Any force on the bodies inside the system from bodies outside the system is called an external force.
• If the bodies in the system are connected rigidly, the external forces are used to calculate the net force and the internal forces are ignored.

SOME PARTICULAR FORCES

GRAVITATIONAL FORCE

• A force that pulls the body directly to the center of the earth is called the gravitational force.
• The gravitational force is equal to the product of mass and the acceleration of free-fall.
• When a body is at rest, the gravitational force does not disappear, it is just canceled by another force on the same body.

WEIGHT

• The weight of a body is the magnitude of the net force required to prevent the body from falling freely, as measured by someone on the ground.
• It is equal to the gravitational force since it is caused by it, therefore it is also a product of mass and the acceleration of free-fall.
• The weight of a body can be measured by a Newton meter, and it has to be remembered that weight and mass are different.

NORMAL FORCE

• The force of equal magnitude that acts opposite to the downward force of gravity on the same object to stabilize it is called the normal contact force.

• When a body presses against a surface, the surface (even a seemingly rigid one) deforms and pushes on the body with a normal force that is perpendicular to the surface.

• It is also equal to the product of mass and acceleration of free-fall.

  FRICTION

• The resistance that a body faces over a surface is said to be a single force of friction/frictional force.

• It always opposes motion.

• Sometimes, for simplicity, it is said to be negligible.

TENSION

• When a cord (or a rope, cable, or other such object) is attached to a body and pulled taut, the cord pulls on the body with a force directed away from the body and along the cord. This force is usually called tension.
• The mass of the cord is said to be negligible.

NEWTON’S THIRD LAW

• Two bodies are said to interact when they push or pull on each other—that is when a force acts on each body due to the other body.
• Newton’s third law of motion states that when two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.
• The interacting bodies are called the third-law force pair.