What is the relation if any between the force acting on an object and the direction in which the object is moving?

Mass or Inertia and Newton's First Law

Force, Velocity and Acceleration, Vector Quantities in Newton's Laws

• Newton's First Law is the law of inertia. An object with no net forces acting on it which is initially at rest will remain at rest. If it is moving, it will continue to move in a straight line with constant velocity.
• Forces are "pushes" or "pulls" on the object, and forces, like velocity and acceleration are vector quantities.
• Vectors have magnitude and direction.
• Adding two forces gives a resultant or net force represented by a third vector. The rule for adding two vectors is to put the tip of the first vector on the tail of the second vector to form the third vector which extends from the tail of the first vector to the tip of the second. (See Figure 2-8 and animation of vector addition in Explore Science.) Click on Adding Vectors. Adding Vectors
• Now we come to the case when the net force on an object is not zero. Newton's Second Law states: F = ma. F is the net force acting on an object. m is its mass. a is its acceleration.
• What is the relationship between mass and weight based on Newton's Second Law? Mass is a property of an object. It depends on the amount of "stuff" in it. But weight is a force that depends on the strength of gravity. That is why objects weigh about 1/6 as much on the moon as they do on earth. On earth, the weight of an object is given by W = Mg, where M is its mass and g is the acceleration due to earth's gravity. Newton' second law says that object of mass M experiences a force W (its weight) and a downward acceleration g.

A Closer Look at Newton's Second Law

• Newton's Second Law, F = ma is a vector equation. It says that the net force (a vector) acting on a mass m (a number) causes an acceleration (a vector) of the object in the same direction as the net force.
• The net force is the combined force of all individual forces acting on an object.
• Newton's First Law can be seen to be the special case in the Second Law when F, the net force, is zero. When that happens, the acceleration a must also be zero. Since acceleration is given by the change of velocity divided by elapsed time, the velocity doesn't change.

Summary: Newton's First and Second Laws of Motion

• Newton's First Law:
  If no net force acts on an object it remains at rest, if initially at rest, or it maintains its velocity if initially in motion.
• Newton's Second Law: F = ma:
  The net force F acting on an object with mass m and acceleration a is given by this expression.
• Newton's first law is a special case of Newton's second law when F = 0. Since m is not zero, acceleration must be zero. Hence, the velocity must remain contant. An object at rest is one with zero velocity.

Mass and Weight

1. Weight of object W is the force exerted ON the object by earth's gravitational field.
2. Apply Newton's Second Law to Free Falling Object (neglect air resistance): W = mg, where W = F and g = a.
3. Force and acceleration are vectors, so W and a are vectors and they must point in the same direction.

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