**Concept of Force**

· 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 constant

velocity 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.

**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*v " 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

**The Gravitational Force and Weight**

• The attractive force exerted by the Earth on an object is called

**the gravitational force**• The gravitational force exerted on an object is equal to the product of its mass (a scalar quantity) and the free-fall acceleration:

•

*The weight of an object is the*magnitude of the gravitational force acting on the object.**ANSWER**

• 5.5 (a). The gravitational force acts on the ball at

*all points in*its trajectory.• 5.6 (b). Because the value of

*g is smaller on the Moon than*on the Earth, more mass of gold would be required to represent 1 newton of weight on the Moon. Thus, your friend on the Moon is richer**Newton’s third law**

Newton’s third law states that if two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1 Thus, an isolated force cannot exist in nature.

**Some Applications of Newton’s Laws**

·

**Objects in Equilibrium**•

**Objects Experiencing a Net Force**A crate being pulled to the right on a frictionless surface. The free-body diagram representing the external forces acting on the crate

**Forces of Friction**

Experimentally, we find that, to a good approximation, both

*fs,max and fk are proportional*to the magnitude of the normal force. The following empirical laws of friction summarize the experimental observations:• The magnitude of the force of static friction between any two surfaces in contact can have the values

where the dimensionless constant -

*s is called the coefficient of static friction and n is the magnitude of the normal force exerted by one surface on the other. The*equality in Equation 5.8 holds when the surfaces are on the verge of slipping, that is, whenThis situation is called

*impending motion. The inequality*holds when the surfaces are not on the verge of slipping.• The magnitude of the force of kinetic friction acting between two surfaces is

Where

*is the coefficient of kinetic friction. Although the coefficient of kinetic*friction can vary with speed, we shall usually neglect any such variations in this text

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