# What is the difference between a force and a net force?

I read in Newton's first law, it states that an object will continue to have a constant velocity unless acted upon by a force whilst for other articles, it states "unless acted upon by a net force." Which one is correct? Are they both interchangeable? Is there any difference between these two concepts?

"Net force" simply means the sum of all forces. The "unless acted upon by a net force" version is more correct. For example, as you stand or sit still, the earth pushes you up with a force equal and opposite to the force with which gravity pulls you down. The net force, or total force, is zero, so you do not move.

• More specifically the sum of one force is the force itself (which is the first wording) and when more than one force the second wording applies. Jun 22 '20 at 16:28
• No, this is the reverse of the common misunderstanding of the 3rd law. To get the net force, you need to add up all forces that act on one body, but you’re adding up forces acting on different bodies. Gravity pulls you down and the chair pushes you up, this is what needs to be summed. Jun 23 '20 at 1:07
• Thank you Roman - I had been thinking of gravity versus the normal force, as you said, but wrote something else and don't know how I misstated it like that. I've edited it to correct this. Jun 23 '20 at 2:04

The wordings of Newton's laws differ, although the math stays the same.

A "net force" is an English phrasing for the sum of all forces. Intuitively, if I push on a wood block on one side with 100N, you push on the block from the other side with a force of 100N, the block isn't going to go anywhere. While there are multiple 100N forces being applied, the sum of the forces (or the "net force" on the block) is zero, so it remains at rest.

The terms are not actually interchangeable. Mathematically, one is $$F_i$$ and the other is $$\sum_{i=0}^N F_i$$. However, we are talking about communicating in English. In many cases, people will assume that the word "net" can be implied, and will omit it. This is especially true in simple textbook examples where there may be only one force acting on the body.

The word net means total, or sum

Here is a scenario: A rolling cart with some forces acting along its direction of motion. Now consider the following situations

1. No forces acting upon the cart. The net force is zero and the cart moves with constant velocity. $$F_{\rm net} = 0$$

2. One force $$F_1$$ acts on the cart. The net force equals this force and the cart accelerates. $$F_{\rm net} = F_1 \neq 0$$

3. Two or more forces $$F_1$$, $$F_2$$, etc act on the cart. The net force is the "directional" sum of the forces. This sum is not zero, and the cart accelerates. $$F_{\rm net} = F_1 + F_2 + \ldots \neq 0$$

4. Two equal and opposite forces act on the cart, $$F_1=F$$ and $$F_2=-F$$. The net force is zero and the cart moves with constant velocity $$F_{\rm net} = F_1 + F_2 = F - F = 0$$

5. Two or more forces $$F_1$$, $$F_2$$, etc act on the cart but they all balance out. The net force is zero and the cart moves with constant velocity. $$F_{\rm net} = F_1 + F_2 + \ldots = 0$$

So the more general term the describes the situation is net force and only when there is one force acting the two wordings are equivalent.

It means the same thing, but is worded more precisely.

The difference becomes clearer when you consider two forces that are applied to the object at the same time - in the less precise wording, of course there would be an acceleration, because there is a force (and another one for the second force). What really happens is that the (vectorial) sum of the two forces - the net force - decides if there will be an acceleration.

The term net force clarifies that you need to add up all forces (if more than one), and if there is a sum = net force, an acceleration will happen.

• So if the sum is greater or less than zero, there'll be an acceleration? Jun 22 '20 at 16:24

Besides the answers already given, you can think of Newton's first law as a special case of Newtons second law. For Newton's second law the "force" is explicitly stated as a "net force", or

$$F_{net}=ma$$

Assuming constant mass, if the net external force acting on an object is zero, then the acceleration of the object is also zero, i.e., the object will either be at rest or moving at constant velocity with respect to an observer in any inertial frame per Newton's first law.

Hope this helps.

[...] whilst for other articles, it states "unless acted upon by a net force."

The latter is really the correct expression, the former really being a 'lazyism'.

Consider the following body, subject to three forces as an example:

Newton's First Law refers to the net force $$\mathbf{F}$$, calculated as the vector sum:

$$\mathbf{F}=\displaystyle\sum_{i=1}^n\mathbf{F_i}=\mathbf{F_1}+\mathbf{F_2}+\mathbf{F_3}$$

The individual forces, in that sense, don't matter, only the so-called resultant force matters.

Force is a vector quantity. The first law talks of a single object and a force, without going in the details.

A net force means a vector addition of forces, two equal and opposite forces add up to zero net force . This is expressed more clearly here.