# Question about inertia and acceleration

1. Nov 27, 2013

### FieldvForce

This question is just about a thought I was having.

If a 1 kg object which is at rest is made to accelerate with a force of 20 newtons and then three seconds later have an opposing force of 20 N applied to it with an impulse of (1)60/(T=0), would the object begin to accelerate in the opposite direction?

2. Nov 28, 2013

### CWatters

Tell us what you think will happen.

3. Nov 28, 2013

### FieldvForce

Well the inertia of the object opposes change in motion and that is what the forward force is causing, if the backward force removes the foward acceleration instantaneously more force than necessary is used to make Fnet = 0 and so Fnet is negative and large.

4. Nov 28, 2013

### sophiecentaur

What counts here is Impulse. Work out the initial impulse. Is it greater or less than the second impulse applied.

There will be no acceleration once the forces have stopped, will there? Think Newton for every stage. The term "Inertia" is not really applied to these simple problems. If you mean Mass, say Mass and if you mean Momentum, say Momentum and follow the rules, rather than trying to 'chat' through the problem.

5. Nov 28, 2013

### FieldvForce

I am trying to understand the problem so that I can apply the rules, I don't think i have the brain power to 'chat' through the problems as most who are brave enough to stop clinging to the rules for one moment are usually classed as geniuses further down the line.

Maybe the way I presented the situation was inaccurate.

An object with mass 1 kg is acted upon by a force of 20 N, after three seconds an opposing force of 20 N is applied over a time T= 0.

So that the impulse is 0 and the velocity should immediately become constant. Will with object begin to accelerate backwards due to the inertia already apposing the forward acceleration?

6. Nov 28, 2013

### CWatters

If you apply a force for zero duration it has no effect.

7. Nov 28, 2013

### Staff: Mentor

Still unclear. The initial force of 20 N is applied for three seconds? Is it removed after three seconds?

Saying that an opposing force of 20 N is applied for 0 seconds is another way of saying that no opposing force was applied. Try again.

The velocity will be constant when the net force is zero. Did you remove the initial force?

8. Nov 28, 2013

### FieldvForce

You have to constantly apply the force? I thought tF=mv ∴ if T = 0 impulse = 0 and F = ∞

ΔF/ΔT, where ΔT = 0, however.
ΔF will also = 0 since the forces cancel obviously there is an issue with dividing by 0, ΔT is just meant to be extremely small, but this is really about the inertia of the object.

9. Nov 28, 2013

### Staff: Mentor

So now the opposing force is infinite, not merely 20 N? But still applied for zero time?

Just state the real force (finite) applied for some finite time. Then you'll be able to find the impulse it delivers.

10. Nov 28, 2013

### FieldvForce

The less time the force is applied the larger it must be to have the desired affect.

Right, 20 N of force is applied for half a second. Then an opposing 20 N is applied for 0.5 immediately (this is why I was talking about 0 seconds) after the first force is removed; will object accelerate in the opposite direction due to the inertia of the object and the opposing 20 N.

Can the inertia act as an opposing force along with the opposing 20 N causing the 20 N to be excessive in terms of causing the object to have constant velocity.

11. Nov 28, 2013

### Staff: Mentor

OK.

As long as there is a net force on the object, it will accelerate. While the initial force acts, the object accelerates in the direction of that force. When that force is removed and the opposing force acts, the object will accelerate in the direction of that new force.

In this case, assuming the object started from rest it will end up at rest, since the two impulses are equal and opposite. The first force speeds it up; the second force slows it back down.

I don't know what you mean.

12. Nov 28, 2013

### Staff: Mentor

As a wise person once recommended to you a long time ago, the term "inertia" is too vague to be of use in this discussion. It can either mean mass (in which case use the term "mass") or it can mean momentum (in which case use the term "momentum").

Assuming that you mean mass then the answer to your first question is: yes, according to f=ma the object will accelerate in the opposite direction in response to a net force in the opposite direction. Under the same assumption the answer to your second question is: no, mass cannot act as force, they have different units.

13. Nov 28, 2013

### FieldvForce

Ah I see what he meant now, both the mas and the momentum can act to appose a change velocity.

14. Nov 28, 2013

### CWatters

Consider two objects with the same momentum but different mass. It will take the same impulse to stop them.

15. Nov 28, 2013

### sophiecentaur

No. I can see that you are still wanting to describe the effects of force on motion in the pre-Newtonian way. This approach was put aside long ago because of its limits. The whole business of Dynamics (as we used to call it) is essentially a Quantitative thing and the Maths is needed, even at an initial level. Mass needs Force to accelerate it. Putting N2 this way round: a = F÷m, shows that the force is 'divided up' between the elements of mass in an object. N3 says that the reaction is in a direction acting against the force.
Momentum doesn't "oppose" the force, it is just changed 'by' the force being applied for a finite time. (That's Impulse). However fast an object is moving (whatever its momentum), in a given direction, a Force on it will produce exactly the same acceleration on it (Force = rate of change of Momentum) and remember all this involves Vectors and the directions are important.
It may be tiresome but using the well known equations always gives the right answer in this sort of situation (non-relativistic etc. etc.).

16. Nov 28, 2013

### FieldvForce

After reading these posts and thinking for a while I have found that I made quite a mistake and misunderstood the natures of force and momentum.

I aslo mistook this equation F = mΔv/Δt as meaning an change in momentum in close 0 seconds results in a massive as apposed to a change in momentum in close to 0 seconds requires a massive force.

So considering the situation now.

20 N has to be applied over some defined time, as apposed to applied for an infinitesimal period as this would mean no change in momentum and thus no force applied at all.

If the initial force is removed forward acceleration no longer continues and the objects mass (inertia) opposes the change in motion caused by the second force, if the initial force is not removed and the second force is applied the sum of forces acting on the object is 0 and so the acceleration is 0.

One question, is the mass (inertia) of the object only observable when the object is not in equilibrium? I think that was the question beneath my thought processes before I posted this thread.

Last edited: Nov 28, 2013
17. Nov 28, 2013

### sophiecentaur

It can be in equilibrium under gravitational forces of course.

18. Nov 28, 2013

### FieldvForce

Orbiting objects?

19. Nov 28, 2013

### sophiecentaur

I was thinking of a mass resting on a table. Gravity and equilibrium.

20. Nov 28, 2013

### Staff: Mentor

Orbiting objects are not in equilibrium.