Question

1. Calculate the net resultant force in each case and also mention the direction in which the box will move.
10N 15N 5N 2N 3N
3N 7N
(a) (b) (c)

Answer 1

Answer:

Explanation:

If we know the mass m of an object and the acceleration a produced by the forces that act on it, we can find the resultant force using Newton's Second Law. Indeed, according to Newton's Second Law, the force F that alone produces the acceleration a on an object of mass m is:

F = ma

This force F is our resultant force. So, we can write:

R = ma

Which indicates that the resultant force R has the same direction as a, and has magnitude equal to the product ma.

For example, if a box of 1.5 kg is subject to 5 forces which make it accelerate 2.0 m/s2 north-west, then the resultant force is directed north-west and has the magnitude equal to 1.5 kg × 2.0 m/s2 = 3.0 N.

Often, however, we know the forces that act on an object and we need to find the resultant force.

Experiments show that when an object is subject to several forces, F1, F2, ..., the resultant force R is the vector sum of those forces:

R = F1 + F2 + ...

Notice that this is not a mere sum of the magnitudes of the forces, but the sum of the forces taken as vectors, which is more involved because vectors have both a magnitude and a direction that we need to consider when doing the sum.

According to the above equation, if an object is subject to no forces, then the resultant force is zero, and if an object is subject to only one force, then the resultant force is equal to that force. These two cases are pretty simple, but what about an object subject to two or more forces? How do we perform the vector sum then?

To explain this clearly, we will now go through all the cases that can happen, from simple ones in which all the forces are parallel, to more complex ones in which the forces are not parallel, and show how to find the resultant force in each of them with the help of examples.