## Senin, 14 November 2011

### The Law of motion

5.5 The Gravitational Force and
Weight
The attractive force exerted by the Earth on an object is called the gravitational force Fg . Applying Newton’s second law ∑ F =ma to a freely  falling object of mass m, with a =g  and F =Fg , we obtain:
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.

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 .
Thus, the weight of an object, being defined as the magnitude of Fg , is equal to mg.
Because it depends on g, weight varies with geographic location. Because g decreases with increasing distance from the center of the Earth, objects weigh less at higher altitudes than at sea level.
5.6 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.

This is such an important and often misunderstood concept that it will be repeated here in a Pitfall Prevention. Newton’s third law action and reaction forces act on different objects. Two forces acting on the same object, even if they are equal in magnitude and opposite in direction, cannot be an action–reaction pair.
5.7 Some Applications of Newton’s Laws
Remember that when we apply Newton’s laws to an object, we are interested only in external forces that act on the object .
For illustration: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

A.    Objects in Equilibrium

If the acceleration of an object that can be modeled as a particle is zero, the particle is
in equilibrium. Consider a lamp suspended from a light chain fastened to the ceiling,
as in Figure 5.7a. The free-body diagram for the lamp (Figure 5.7b) shows that the
forces acting on the lamp are the downward gravitational force Fg and the upward
force T exerted by the chain.
The condition:  ∑Fy = may =0 gives
∑ Fy = T - Fg = 0     or        T =Fg
A.    Objects Experiencing a Net Force

If an object that can be modeled as a particle experiences an acceleration, then there
must be a nonzero net force acting on the object.
We can now apply Newton’s second law in component form to the crate. The only force acting in the x direction is T. Applying  ∑Fx =max to the horizontal motion gives

Figure 5.8 (a) A crate being
pulled to the right on a frictionlesssurface. (b) The free-body diagram representing the external forcesacting on the crate.
5.8 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, when
This 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   µk 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.