**5.5 The Gravitational Force and**

**Weight**

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

The gravitational force exerted on an object is equal to the product of its mass (a scalar quantity) and the free-fall acceleration: *g .*Applying Newton’s second law ∑ F =*ma to a freely*falling object of mass*m, with a =g and*∑*F =Fg , we obtain:**The weight of an object is the*magnitude of

**the gravitational force acting on the object.**

The Answer are….

• 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 F

*g , 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 F

*g*and the upwardforce 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, 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

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

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