Newton's Laws

---

Interactions among things or matters occur by forces. Forces cause motion and influence the basic kinematics of objects and they are important to study mechanics.
Newton is the father of classical mechanics and has stated 3 laws dealing with forces:

1. F = ma (m = mass, a = acceleration)
2. For every force, there MUST also be an equal and opposite force
3. All objects have inertia; that is, an object will remain at rest or in uniform motion unless acted upon by some outside force

When solving problems involving force, a force diagram is drawn on the object which forces are acted upon. Then to compute the resulting acceleration, these forces are combined accordingly calculating the y-components and x-components of the vectors. Or to find the original force which resulted in acceleration of some object, the equation is simply manipulated to fit the situation.

This diagram shows forces that are in the box - ball system on a frictionless table. For the box, there is the weight which is equivalent to mass times g for gravitational acceleration. And then there are two normal forces which are denoted by the letter N. Normal forces are the forces perpendicular (normal) to the surface. These exist on any surface that are in contact with another. N_t is the normal force exerted by the table, and N_cis the normal force exerted by the ball. Same forces act on the ball except in different magnitudes. The coordinate axes for positive x and y directions are included in the diagram also. This is to give reference to directions for the force vectors. Any coordinate system suitable for the unique force diagrams may be used. But generally the positive directions for x and y are generally in the direction of the resulting accelerations.

Now we compute to find out the resulting accelerations of two objects:
-Box-
SF_x: N_c = Ma_x
SF_y: N_t - Mg = Ma_y
a_x = N_c/M
a_y = 0 (N_t = Mg, Newton’s 2^nd Law)

-Ball-
SF_x: N_b = ma_x
SF_y: N_t - mg = ma_y
a_x = N_c/m = N_c/m (N_t=mg, Newton’s 2^nd Law)
a_y = 0 (N_t = mg, Newton’s 2^nd Law)

Sample Problem
What is the resulting horizontal acceleration of an object (mass = m) if a force F at angle q (theta, measured from the horizontal) is exerted on the object?

Your Answer:

Solution