# Question #2f185

Jun 5, 2016

Any body may be acted upon by a number of forces in different directions. Forces add up or cancel each other either fully or partially. The net force is the amount of force that is effective on the body. The net force is not the actual amount of force acting on it. It is the sum of the forces acting on the body.

#### Explanation:

Forces obey the principle of superposition, i.e. the the resultant force at any point in space is equal to the vector sum of all the forces acting at the point.

For example, considering an object kept on the table top, it is acted upon by gravity but it is still in rest. It is due to the equal and opposite normal force due to the table. In this case, two forces act on the body, but there's no net force as one totally cancels the other.

When you're pushing a box on the floor, it is acted by the frictional force due to the floor and by the force you exert on it. Gravity and Normal reaction are among other forces. The force you exert overpowers the frictional force. The frictional forces partially cancels the force you have been exerting. Gravity and Normal reaction totally cancel each other in this case.
The box is acted upon by so many forces but the net force on it is the partially cancelled force you've been exerting on the body. The partial cancellation comes due to the friction which opposes your force.

Another point to note is that if there's a net force on the body, the body is sure to accelerate. It'll either gain or lose speed.

Jun 5, 2016

The net force is the vector sum of all the forces acting on an object.

#### Explanation:

Whenever a number of forces act on an object, and if the vector sum of all the forces is not balanced, then we have a resultant force. This is called net force. A net force is capable of accelerating a mass. The acceleration could be linear or circular or both.

In equilibrium state net force acting on an object is zero. The object does not accelerate.

In the figure below force $\vec{F}$ acts at a point H of a free rigid body. The body has the mass $m$ with its center of mass at point C.

The net force causes changes in the motion of the object described by the following expressions.

1. Linear acceleration of center of mass $\vec{a} = \frac{\vec{F}}{m}$;
where $\vec{F}$ is the Net Force and $m$ is mass of the object
2. Angular acceleration of the body $\vec{\alpha} = \frac{\vec{\tau}}{I}$,
where $\vec{\tau}$ is the resultant torque and $I$ moment of inertia of the body.
Torque, a vector quantity is caused by a net force $\vec{F}$ defined with respect to some reference point $\vec{r}$ as below
$\setminus \vec{\setminus} \tau = \setminus \vec{r} \setminus \times \setminus \vec{F}$
or $| \setminus \vec{\setminus} \tau | = k | \setminus \vec{F} |$