Dynamic of mas point

slowing down, what is the direction of the force on

the car that causes it to slow down? (a) eastward (b) westward (c) neither of these.

Quick Quiz 2 A ball is thrown upward. While the ball is in free fall, does its acceleration (a) increase (b) decrease (c) increase and then decrease (d) decrease and then increase (e) remain constant?

Quick Quiz 3 After a ball is thrown upward and is in the air, its speed (a) increases (b) decreases (c) increases and then decreases (d) decreases and then increases (e) remains the same.

and rigid body. Newton’s laws. Mass. Force. Forces in mechanics.

Gravitational forces. The law of gravity. Elastic forces. Friction forces. Circular Motion and Other Applications of Newton’s Laws.

acceleration without considering what might cause that motion. Now we

consider the cause—what might cause one object to remain at rest and another object to accelerate? The two main factors we need to consider are the forces acting on an object and the mass of the object. We discuss the three basic laws of motion, which deal with forces and masses and were formulated more than three centuries ago by Isaac Newton. Once we understand these laws, we can answer such questions as “What mechanism changes motion?” and “Why do some objects accelerate more than others?”

are all field forces:
gravitational forces between objects,
electromagnetic forces

between electric charges,
nuclear forces between subatomic particles, and
weak forces that arise in certain radioactive decay processes.

In classical physics, we are concerned only with gravitational and electromagnetic forces.

is possible to identify a reference
frame in which the object

has zero acceleration.

Moving object can be observed from any number of reference frames. Newton’s first law of motion, sometimes called the law of inertia, defines a special set of reference frames called inertial frames. This law can be stated as follows:

Newton’s First Law and Inertial Frames

reference.
Any reference frame that moves with constant velocity relative to

an inertial frame is itself an inertial frame.

Newton’s First Law and Inertial Frames

the object is zero.
In the absence of external forces, when

viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).

Newton’s First Law and Inertial Frames

much resistance an object exhibits to changes in its velocity,

and the SI unit of mass is the kilogram. The greater the mass of an object, the less that object accelerates under the action of a given applied force.

accelerations a given force produces on different objects. Suppose a

force acting on an object of mass m1 produces an acceleration a1, and the same force acting on an object of mass m2 produces an acceleration a2. The ratio of the two masses is defined as the inverse ratio of the magnitudes of the accelerations produced by the force:

(2.1)

Mass

independent of the object’s surroundings and of the method used

to measure it.

Also, mass is a scalar quantity and thus obeys the rules of ordinary arithmetic. That is, several masses can be combined in simple numerical fashion. For example, if you combine a 3-kg mass with a 5-kg mass, the total mass is 8 kg. We can verify this result experimentally by comparing the accelerations that a known force gives to several objects separately with the acceleration that the same force gives to the same objects combined as one unit.

Mass

are two different quantities. The weight of an object is

equal to the magnitude of the gravitational force exerted on the object and varies with location. For example, a person who weighs 180 lb on the Earth weighs only about 30 lb on the Moon. On the other hand, the mass of an object is the same everywhere: an object having a mass of 2 kg on the Earth also has a mass of 2 kg on the Moon.

Mass

no forces act on it. It either remains at rest

or moves in a straight line with constant speed. Newton’s second law answers the question of what happens to an object that has a nonzero resultant force acting on it.

Newton’s Second Law

of ice across a frictionless horizontal surface. When you exert

some horizontal force F on the block, it moves with some acceleration a. If you apply a force twice as great, you find that the acceleration of the block doubles. If you increase the applied force to 3F, the acceleration triples, and so on. From such observations, we conclude that the acceleration of an object is directly proportional to the force acting on it.

Newton’s Second Law

as stated in the preceding section. We can understand this

by considering the following experiment. If you apply a force F to a block of ice on a frictionless surface, the block undergoes some acceleration a. If the mass of the block is doubled, the same applied force produces an acceleration a/2. If the mass is tripled, the same applied force produces an acceleration a/3, and so on.

Newton’s Second Law

the acceleration of an object is inversely proportional to its

mass. These observations are summarized in Newton’s second law:

When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Newton’s Second Law

following mathematical statement of Newton’s second law:
(2.2)
In both the textual

and mathematical statements of Newton’s second law above, we have indicated that the acceleration is due to the net force acting on an object. The net force on an object is the vector sum of all forces acting on the object. In solving a problem using Newton’s second law, it is imperative to determine the correct net force on an object. There may be many forces acting on an object, but there is only one acceleration.

Newton’s Second Law

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:

(2.3)

Unit of Force

your fingertip, the book pushes back and makes a small

dent in your skin. If you push harder, the book does the same and the dent in your skin is a little larger. This simple experiment illustrates a general principle of critical importance known as Newton’s third law:

If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 on object 1:

(2.5)

Newton’s Third Law

force cannot exist. The force that object 1 exerts on

object 2 may be called the action force and the force of object 2 on object 1 the reaction force. In reality, either force can be labeled the action or reaction force.

Newton’s Third Law

The action force is equal in magnitude to the reaction force and opposite in direction. In all cases, the action and reaction forces act on different objects and must be of the same type.

we are interested only in external forces that act on

the object.

For now, we also neglect the effects of friction in those problems involving motion; this is equivalent to stating that the surfaces are frictionless.

In problem statements, the synonymous terms light and of negligible mass are used to indicate that a mass is to be ignored when you work the problems. When a rope attached to an object is pulling on the object, the rope exerts a force T on the object, and the magnitude T of that force is called the tension in the rope. Because it is the magnitude of a vector quantity, tension is a scalar quantity.

that can be modeled as a particle is zero, the

particle is in equilibrium.

forces. All forces can be divided to 2 main types:

forces, acting at the direct contact, and forces, acting independently whether bodies contact or not, i.e. forces, which can act on the distance.

Compressions, tensions, flexions etc. are the form or volume change in compare to its initial state. Such changes are called deformations.

Forces, disappearing with disappearing of deformations, called elastic forces.

Forces of Friction

of another type so called forces of friction.

The main

feature of forces of friction is that they prevent the movement of every of contact bodies respectively to another one or prevent appearing of this movement.

Forces of Friction

from moving acts to the left and is called the

force of static friction fs. As long as the trash can is not moving, fs = F.

Fig. 1 – Example of force of friction

Forces of Friction

two surfaces in contact can have the values
where the dimensionless

constant is called the coefficient of static friction and n is the magnitude of the normal force exerted by one surface on the other.

At the same time with changing of direction of force F the direction of force of friction also changes. Thus module and direction of force of friction are defined by module and direction of that external force, which it balanced: force of static friction equals on module and opposite to direction of that external force, which approaches to cause the slipping of one body on another one.

(2.6)

Forces of Friction

the force of kinetic friction fk .
Fig. 1 –

Example of force of friction

Forces of Friction

two surfaces is
where is the coefficient

of kinetic friction.

(2.7)

Table 1. Coefficients of Friction

path of radius r experiences an acceleration that has a

magnitude:

The acceleration is called centripetal acceleration because ac is directed toward the center of the circle. Furthermore, ac is always perpendicular to v.

Newton’s Second Law Applied
to Uniform Circular Motion

circular path in a horizontal plane. A force Fr directed

toward the center of the circle keeps the ball moving in its circular path.

If we apply Newton’s second law along the radial direction, we find that the net force causing the centripetal acceleration can be evaluated:

(2.8)

path, there is, in addition to the radial component of

acceleration, a tangential component having magnitude dv/dt. Therefore, the force acting on the particle must also have a tangential and a radial component. Because the total acceleration is


the total force exerted on the particle is



The vector is directed toward the center of the circle and is responsible for the centripetal acceleration. The vector ttt tangent to the circle is responsible for the tangential acceleration, which represents a change in the speed of the particle with time.

(2.9)

Nonuniform Circular Motion

to the end of a cord of length R and

set into motion in a vertical circle about a fixed point O. Determine the tension in the cord at any instant when the speed of the sphere is v and the cord makes an angle θ with the vertical.

a curved exit ramp. What causes a front-seat passenger to

move toward the right-hand door? (b) From the frame of reference of the passenger, a force appears to push her toward the right door, but this is a fictitious force. (c) Relative to the reference frame of the Earth, the car seat applies a leftward force to the passenger, causing her to change direction along with the rest of the car.

a car moving in a circular path? (a) the car

has tangential acceleration but no centripetal acceleration. (b) the car has centripetal acceleration but no tangential acceleration. (c) the car has both centripetal acceleration and tangential acceleration.

Quick Quiz 1 If a fly collides with the windshield of a fast-moving bus, which object experiences an impact force with a larger magnitude? (a) the fly (b) the bus (c) the same force is experienced by both.

Quick Quiz 2 In a free-body diagram for a single object, you draw (a) the forces acting on the object and the forces the object exerts on other objects, or
(b) only the forces acting on the object.