Chapter 5 The Law of Motion (Part 1)

Concept of Force

Everyone has a basic understanding of the concept of force from everyday experience.

When you push your empty dinner plate away, you exert a force on it. Similarly, you exert a force on a ball when you throw or kick it. In these examples, the word force is associated with muscular activity and some change in the velocity of an object. Forces do not always cause motion, however. For example, as you sit reading this book, a gravitational force acts on your body and yet you remain stationary.As a second example, you can push (in other words, exert a force) on a large boulder and not be able to move it.

 

·         The net force acting on an object is defined as the vector sum of all forces acting on the object.

·         If the net force exerted on an object is zero, the acceleration of the object is zero and its velocity remains constant. When the velocity of an object is constant (including when the object is at rest), the object is said to be in equilibrium.

Measuring the Strength of a Force

Newton’s First Law and Inertial Frames

If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration.

An inertial frame of reference is one we can identify in which an object that does not interact with other objects experiences zero acceleration. Any frame moving with constantvelocity relative to an inertial frame is also an inertial frame. Newton’s first law states that it is possible to find such a frame, or, equivalently, in the absence of an external force, when viewed from an inertial frame, an object at rest remains at rest and an object in uniform motion in a straight line maintains that motion.

5.1 (d). Choice (a) is true. Newton’s first law tells us that motion requires no force: an object in motion continues to move at constant velocity in the absence of external forces. Choice (b) is also true. A stationary object can have several forces acting on it, but if the vector sum of all these external forces is zero, there is no net force and the object remains stationary.

Definition of Equilibrium

If the net force exerted on an object is zero, the acceleration of the object is zero and its velocity remains constant. That is, if the net force acting on the object is zero, the object either remains at rest or continues to move with constant velocity. When the velocity of an object is constant (including when the object is at rest), the object is said to be in equilibrium.

The vector nature of a force is tested with a spring scale. (a) A downward force F1 elongates the spring 1.00 cm. (b) A downward force F2 elongates the spring 2.00 cm. (c) When F1 and F2 are applied simultaneously, the spring elongates by 3.00 cm. (d) When F1 is downward and F2 is horizontal, the combination of the two forces elongates the spring:
 = 2.24 cm

MASS

• Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity   
•  The SI unit of mass is kilogram (kg)
  
  •      mass is a scalar quantity
         example : 3kg + 5kg = 8kg
  •      Mass and weight are two different quantities
          example :
             1. a person who weighs 180 lb on the Earth weighs only about 30 lb on the
                 Moon
   2. an object having a mass of 2 kg on the Earth also has a mass of 2 kg on
       the Moon.
  
  
  Newton’s second law
  
  
  Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The net force acting on an object equals the product of its mass and its acceleration: 
  

    If the object is either stationary or moving with constant velocity, then the object is in equilibrium and the force vectors must cancel each other. 
  
  
  

  

  
   
  
  
  
  
  
  
  
  
  
  ANSWERS
  
  
  5.2 (a). If a single force acts, this force constitutes the net force and there is an acceleration according to Newton’s second law.
  
  
  
  
  5.3 (c). Newton’s second law relates only the force and the acceleration. Direction of motion is part of an object’s velocity,and force determines the direction of acceleration, not that of veis constant, and the speed of the object (starting from rest) is given by v² at. With twice the acceleration, the object will arrive at speed v at half the time.locity.
  
  
  5.4 (d). With twice the force, the object will experience twice the acceleration. Because the force is constant, the acceleration.
  
  
  
  
  

  Unit of Force

  The SI unit of force is the newton, which is defined as the force that, when acting on an object of mass 1 kg, produces an acceleration of 1 m/s². From this definition and Newton’s second law, we see that the newton can be expressed in terms of the following fundamental units of mass, length, and time: N = kg . m/s².