# Does constant velocity means no force applied?

If there is a body moving with a constant velocity of $$1000m/s$$ and it’s mass =$$10kg$$.

Then , how is it possible that the force applied by this body$$= 0 N$$since it will definitely make an object in front of it move.

$$F_{applied}$$ $$= 10kg * acc(0) = 0N.$$

EDIT:

• "force applied by this body or on this body" ??? A good diagram will make the question clear.
– AJN
Jun 21 at 12:45
• When two bodies collide, there are (equal and opposite) forces acting on both of them. Jun 21 at 14:39

There are many ways to prove that constant velocity means that the resultant force is zero.

## impulse

constant velocity means that from state 1 to state 2 $$\Delta v_{12} = v_{2} -v_{1} =0$$

Therefore, the change in momentum p is also: $$\Delta p_{12} = \Delta m v_{12} = m\cdot v_{2} -m \cdot v_{1} =0$$

However, the change of momentum is called impulse J in physics $$J = \Delta m v_{12} =0$$

And Impulse is also defined as:

$$J = F\delta t$$

Therefore:

$$J = F\delta t = \Delta m v_{12}$$ $$F= \frac{\Delta m v_{12} }{\delta t } =\frac{0}{\delta t} = 0$$

## Newton's second law.

Because v is constant, therefore acceleration is zero.

Therefore:

$$F= m\cdot a= 0$$

## why does it move the block that comes into contact with

The answer to that is the:

• conservation of momentum (and angular momentum)
• conservation of energy.

When the mass hits the object, what happens is that momentum is conserved. So if mass 2 (object) initially was at rest, it will start to move. In order to move, the mass 1 exerts a force $$F_{12}$$ to the second object.

However that means that the momentum of the mass 1 (10 kg) will change as well. Because of that change the net resultant force exerted will be $$F_{21} = - F_{12}$$.

This is the third law of Newton, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

## Friction

Notice that above, I intentionally write, "resultant force", for the period that the object travels without interacting with mass 2. The reason is that if friction is present, then there is a need for an motive force which is equal and opposite to friction.

• If the motive force is greater than friction, then the object will accelerate.

• If the motive force is less than friction, then the object will decelerate.

In both cases the force is not constant.

• Perfect answer. Thank you Jun 23 at 10:43

Accelerating a frictionless body requires force indeed. However keeping a frictionless body at the same velocity requires no action at all. Imagine a rock floating in space. if you kick it, it will float away at a constant velocity, forever. This is exactly the logic behind the famous first law of Newton, which states that if the net force of an object is 0, the velocity is constant.

However, every body on earth is exposed to some kind of friction (that is, every body that is not contained in a vacuum container, levitated in some way). This friction will constantly slow you down. So unless you keep applying force to the body to compensate for said friction, you cannot keep the velocity constant. Which again refers to Newton's law: the net force is zero. $$F_{net} = 0 = -F_{friction}+F_{external}$$

• Mostly okay, except for kicking the rock. By kicking the rock a force is being applied to the rock.
– Fred
Jun 23 at 8:58