# Staying at rest or moving at a constant velocity

1. Jun 9, 2013

I have two examples.Terminal velocity-When the forces are balanced,the person continues to fall down at a constant velocity.
Holding a Box-When the forces are balanced,the box stays at rest.
A question about power in my text book is:A crane lifts a box of weight 100N up at a constant velocity.The answer used a force of 100N(equal to weight)to lift the box(Stating if the box is moving at a constant velocity the forces are balanced)but sometimes I notice things to stay at rest too(when the forces are balanced).Why is that?Will not the box stay at rest.
The point is, under which circumstances will something move or stay at rest when the forces are balanced?

Last edited: Jun 9, 2013
2. Jun 9, 2013

### Drakkith

Staff Emeritus
If an object is already moving when the forces become balanced, it will keep moving at a constant velocity. If it is not already moving and the forces are balanced, there will be no acceleration and it will not move.

3. Jun 9, 2013

What about the crane example.Did the text book use the correct force.The box stays at rest when in the ground-then how can it move at a constant velocity when the forces become balanced?

4. Jun 9, 2013

### dreamLord

Initially the box was at rest. There was actually some excess force applied at the very beginning by the crane to accelerate the body to a certain velocity v(but this was in an infinitesimally small time interval) . After that the box moved with constant velocity because the force applied by the crane is equal and opposite to that of gravity - since there is no net force, the velocity cannot change, and hence remains fixed at v.

5. Jun 9, 2013

How can you say that?
How can I calculate it?

6. Jun 9, 2013

### tchen

If by "that" you mean why it expended force over a small time interval, it's because there was a change in velocity which implies acceleration which implies a force, since F = ma. This is also how you calculate it if you wanted to (not enough info seems to be given in this problem), you just multiply (change in velocity/change in time)(mass of the body) to get the amount of force necessary to accelerate the body to the given velocity. However, once the velocity is constant, there is no longer a net force that the crane expends and the velocity remains fixed.

7. Jun 9, 2013

Thanks.I have another question
What happens if a ball(Or something)hits on a wall.The wall should exerts a force equal to the force the ball exerts(3rd law of N)(Assuming a person is holding the ball). Why does the ball stop?Will not it move at a constant velocity if the forces are balanced?

8. Jun 9, 2013

### Staff: Mentor

That's true. They exert equal and opposite forces on each other.

It only stops momentarily.

Why do you think the forces are balanced?

9. Jun 10, 2013

A person is holding a ball and bringing it closer to the wall(He is exerting a force on the ball).The ball then touches the wall and stops.Since the force exerted by the wall and the person cancels out,Why does the ball has to stop?According to drakkiths post,If the ball was moving before,it should continue to move..
The person is holding

The wall and the person is exerting forces on the ball(that is equal and opposite)So it cancel out.

Look at the GIF

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Last edited: Jun 10, 2013
10. Jun 10, 2013

### Staff: Mentor

So someone is pushing a ball against a wall? Do not assume that the force exerted by the person and the wall cancels out. To slow the ball down, there is a net force. Once the ball is squashed against the wall, the forces do cancel out and thus the ball stays at rest.

There is no reason to think that the forces exerted on the ball by the person and wall are always equal and opposite. Those forces are not Newton's 3rd law pairs.

What is true is that whatever force the wall exerts on the ball, the ball will exert an equal and opposite force back on the wall. Same for the person and the ball.

What determines the acceleration of the ball is the net force on the ball, which is due to all the forces on it (from the person and from the wall).

11. Jun 10, 2013

The wall exerts a force=to the force the ball exerts which is given by the hand.There is a force on the ball from the wall and from the hand,Which is equal and the hand exerts a force on the right side ob the ball and the wall exerts a force the the left side of the ball.Then why doesn't the forces cancel out?

Last edited: Jun 10, 2013
12. Jun 10, 2013

### Staff: Mentor

Do not assume that the force that the ball exerts on the wall is simply equal to the force that the hand exerts on the ball, as if the ball merely transmits the force from the hand to the wall. That's a reasonable assumption when the ball is in equilibrium, but not while it is accelerating.

13. Jun 10, 2013

I don't understand

14. Jun 10, 2013

### Drakkith

Staff Emeritus
When the ball initially 'contacts' the wall there is a repulsive force between them that gradually builds until it exceeds the force the person is applying. This occurs because in addition to the force the person is applying, the ball also had kinetic energy, which was used to get closer to the wall than equilibrium. Then the ball will move away from the wall until the repulsive force drops below what the person is applying. If all three objects were perfectly rigid and never lost energy, this would continue indefinitely and the ball would oscillate back and forth against the wall.

However, since they aren't perfectly rigid, energy is lost and the ball merely comes to rest instead of oscillating forever.

Or think of it this way. Instead of a person let's put a very small rocket engine on the ball. The rocket engine applies a force and accelerates the ball towards the wall and, if everything were perfectly rigid and lost no energy, the ball would bounce against the wall forever.

15. Jun 10, 2013

Whats drakkith is saying and Doc Al is saying does not quite match.Whats the actual answer i'm confused.
And How can the rocket lose no energy?Does that describe a perpetual machine?

Last edited: Jun 10, 2013
16. Jun 10, 2013

### Drakkith

Staff Emeritus
It can't. Its a hypothetical example. All real world objects would lose energy.

17. Jun 10, 2013

### WannabeNewton

I want to expand upon Doc Al's point. Let's say we have a ball of mass $m$ released from some height $h$ that has a completely inelastic impact with the ground i.e. it loses all its kinetic energy and comes to rest after the impact. More precisely, the momentum immediately before the collision is $p = -mv$ where $\frac{1}{2}mv^{2} = mgh\Rightarrow v = \sqrt{2gh}$ and the momentum immediately after is simply zero. Hence $\Delta p = mv = m\sqrt{2gh}$ and $J = \int _{t_{i}}^{t_{f}}F dt = F_{\text{av}}\Delta t = m\sqrt{2gh}$ where $J$ is the impulse exerted on the ball during the collision (here $\Delta t$ is the duration of the collision). This means the floor exerts an average force $F_{\text{av}} = \frac{m\sqrt{2gh}}{\Delta t}$ on the ball during the collision (we can determine $\Delta t$ using a stopwatch). $F_{\text{av}}$ acts as a sort of retarding force on the ball meaning the ball doesn't immediatly come to rest when it hits the floor; there is some time interval in which the floor exerts a retarding force on the ball and brings it to rest. Once the ball is at rest, we will have achieved static equilibrium i.e. the normal force from the floor acting on the ball will balance out the force of gravity acting on the ball.

You have to be careful with how you apply Newton's 1st law. You can't just use it whilly nilly!

18. Jun 11, 2013

### PeterO

Imagine that instead of attaching the hook/cable of the crane directly to the box, it was attached with a [very thick/strong] rubber band in between the hook and the box.
The crane operator starts the cable/hook moving up at constant speed.
Initially, the rubber band would stretch - and eventually apply a force greater than the weight of the box - causing the box to accelerate up.
The box would have varying acceleration as the rubber-band stretched and contracted but eventually the rubber band may settle in to an appropriate length where the box was now moving up at constant speed, the same speed as the hook.
Now the steel cable on the crane is also elastic - but much stiffer than your average rubber band - so if you attach the hook directly to the box, the cable will stretch slightly [you might not even notice because it is so slight], then contract a bit and oscillate like the rubber band, but relatively quickly reach an equilibrium position. In fact so quickly you may not even notice the variations in speed of the box:- it will look like it just took off at constant speed.
Whether you use a rubber band, or attach the hook directly, eventually the box will be moving up with the crane supplying an upward force equal to the weight of the box. - and eventually may mean a millisecond or two if the crane's cable is thick.

19. Jun 11, 2013

### PeterO

The Wall is exerting a force on the ball - true
The person is exerting a force on the ball - true

What makes you think those two forces are the same magnitude?

Newton's Third Law certainly doesn't claim/predict that.

What Newtons third law says is:

Over on the wall side of the ball - the force of the wall on the ball is the same magnitude, but opposite direction, as force of the ball on the wall.

Over on the person side of the ball - the force of the person on the ball is the same magnitude, but opposite direction, as the force of the ball on the person.

The ball approached the wall at some velocity. If those two forces on the ball [one of the first pair and one of the second pair] are equal, they will balance each other and the acceleration will be zero. If we have some velocity, but zero acceleration, the velocity of the ball will not change.

But the velocity of the ball does change, so the wall must be pushing the ball more strongly than the person.

btw. the two forces acting on the ball - in opposite directions - will cause the ball to distort. If this is a flexible ball - like a basket ball for example - you will even be able to observe that distortion, or at least photograph it with a high speed video camera.

20. Jun 11, 2013