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F=ma doesnt work ? watch

1. Hi everyone,

Basically I was thinking about F=ma and found abit of a problem for which the equation falls down on,

Say there was a lorry mass 1000 kg and it was travelling down a road at 20 ms^-1 but was not accelerating at all it was just travelling at a constant speed, then by Newtons second law the lorry should have a force of 1000 x 0 = 0 N, however if this lorry was to hit a tree for instance, then obviously it is going to hit with a force, a massive force...not a force of 0, could some one explain to me why this is?

Thanks, Chris.
2. You have to think about all of the forces involved, and more importantly, which objects they act on.

In your example, the lorry's engine is providing a forward driving force. This acts on the lorry. As it is travelling at a constant velocity, it is experiencing a drag force against its motion that is equal in magnitude and opposite in direction to the driving force. The resultant force on the lorry is zero.

If the lorry now hits a tree, which of these forces will act on the tree? The driving force will, as it is the force that is trying to accelerate the lorry forwards. But the drag force will not; this force arrises as a result of the lorry's motion. The tree had no motion before it was hit, so this force was not acting on it. Resultant force on the tree during the impact - the driving force of the lorry's engine only.
3. Deceleraton is simply negative acceleration. So, if the lorry comes to rest after impact with the tree in 1s, it has experienced an acceleration of -20 m.s^-2. So by Newton, it has exerts a force on the tree of:

F = 1000*20 = 20,000 N
4. (Original post by cj_134)
Hi everyone,

Basically I was thinking about F=ma and found abit of a problem for which the equation falls down on,

Say there was a lorry mass 1000 kg and it was travelling down a road at 20 ms^-1 but was not accelerating at all it was just travelling at a constant speed, then by Newtons second law the lorry should have a force of 1000 x 0 = 0 N, however if this lorry was to hit a tree for instance, then obviously it is going to hit with a force, a massive force...not a force of 0, could some one explain to me why this is?

Thanks, Chris.
The lorry has ke and momentum. If it hits a tree, then the tree applies a force to the lorry. It has to do this to stop it or slow it down. (newton 2)

This is what Newton's Law states. If the lorry is to be stopped, you have to apply a force. The tree does this.

Because the tree applies a force to the lorry, by Newton 3, the lorry applies an equal and opposite force to the tree.

It is almost certain that this will have the effect of moving the tree and probably knocking it down.
So tree applies force to lorry and this force stops the lorry. (Newton 2)
The lorry applies an equal and opposite force to the tree (Newton 3)
This force flattens the tree. (Newton 2)

I would have to disagree somewhat with Pangol on this.
The lorry will apply a force to the tree irrespective of whether or not the lorry has a driving force. It could just be freewheeling. The presence of a driving force would just mean that the overall force needed to stop the lorry would be greater.
5. (Original post by Stonebridge)
I would have to disagree somewhat with Pangol on this.
The lorry will apply a force to the tree irrespective of whether or not the lorry has a driving force. It could just be freewheeling. The presence of a driving force would just mean that the overall force needed to stop the lorry would be greater.
You are of course correct. That was sloppy thinking on my part.
6. (Original post by cj_134)
Hi everyone,

Basically I was thinking about F=ma and found abit of a problem for which the equation falls down on,

Say there was a lorry mass 1000 kg and it was travelling down a road at 20 ms^-1 but was not accelerating at all it was just travelling at a constant speed, then by Newtons second law the lorry should have a force of 1000 x 0 = 0 N, however if this lorry was to hit a tree for instance, then obviously it is going to hit with a force, a massive force...not a force of 0, could some one explain to me why this is?

Thanks, Chris.
F=ma is a formula for calculating F, the resultant force acting on an object due to acceleration, not its momentum. As you said, the lorry is not accelerating, so it will have a resultant force due to acceleration of 0N as you calculated. However, it will have a linear momentum of 1000kg*20ms^-1 = 20,000Kgms^-1 when it crashes into that tree.
7. Newton's First Law
Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

No resultant force, so either: (a) lorry is at rest and thus remains at rest, or as is your example, (b) lorry continues to move in a straight line with constant velocity (ie 20m/s).

So as your lorry is moving at a constant speed, there is no resultant force acting on it (F = 0N). The lorry has no acceleration as it moves at a constant speed, so m*a = 1000*0 = 0N as well.

0 = 0, and so F = ma
8. the lorry will not hit the tree with any force, the tree will exert a force on the lorry to decelerate it. Then the lorry will exert a contact force or a reaction force on the tree.
9. (Original post by CM23925)
the lorry will not hit the tree with any force, the tree will exert a force on the lorry to decelerate it. Then the lorry will exert a contact force or a reaction force on the tree.
Surely the lorry exerts a force on the tree when it hits it and the tree exerts a force on the lorry to bring its momentum down to 0kgm/s (assuming that the tree is strong enough not to be uprooted by this collision). Besides, what happened to the lorry's driving force? Where did that suddenly go?
10. (Original post by Maths_Lover)
Surely the lorry exerts a force on the tree when it hits it and the tree exerts a force on the lorry to bring its momentum down to 0kgm/s (assuming that the tree is strong enough not to be uprooted by this collision). Besides, what happened to the lorry's driving force? Where did that suddenly go?
The driving force accelerated the lorry up to a speed of 20m/s, and then drag became equal to it, making the resultant 0. This is why the lorry remains at a constant speed; it is Newtons First Law.
11. (Original post by cj_134)
Hi everyone,

Basically I was thinking about F=ma and found abit of a problem for which the equation falls down on,

Say there was a lorry mass 1000 kg and it was travelling down a road at 20 ms^-1 but was not accelerating at all it was just travelling at a constant speed, then by Newtons second law the lorry should have a force of 1000 x 0 = 0 N, however if this lorry was to hit a tree for instance, then obviously it is going to hit with a force, a massive force...not a force of 0, could some one explain to me why this is?

Thanks, Chris.
the forces acting on the body= 0 (the lorry) hence why it isnt accelerating

if it hits something then the lorry will deccelerate, causing a force
12. (Original post by Maths_Lover)
Surely the lorry exerts a force on the tree when it hits it and the tree exerts a force on the lorry to bring its momentum down to 0kgm/s (assuming that the tree is strong enough not to be uprooted by this collision). Besides, what happened to the lorry's driving force? Where did that suddenly go?
Well yes it will exert a force on the tree. But assuming the tree stays where it is. (i.e. doesn't accelerate) then there will be no resultant force applied to the tree. And because the lorry is decelerated then there must be a resultant force applied to the lorry - from the tree. Therefore the only force the lorry applies to the tree will be a contact force. Its just that the force the tree applies to the lorry is much larger than the force that the lorry applies to the tree.

And you aren't thinking about momentum, you're thinking about force. If you are thinking about momentum you are thinking about conservation of momentum. Which just means that if the lorry suddenly stops. Then all the momentum is transferred into the driver, who with a much smaller mass, shoots forwards at a much higher velocity than the lorry was travelling at before the crash. (hence the damage done to the people in a car during a crash).

And the driving force from the engine still exists, assuming it hasn't broken in the crash and the driver is still accelerating. But the force exerted on the lorry from the tree is much greater than the driving force of the engine.
13. (Original post by CM23925)
Well yes it will exert a force on the tree. But assuming the tree stays where it is. (i.e. doesn't accelerate) then there will be no resultant force applied to the tree. And because the lorry is decelerated then there must be a resultant force applied to the lorry - from the tree. Therefore the only force the lorry applies to the tree will be a contact force. Its just that the force the tree applies to the lorry is much larger than the force that the lorry applies to the tree.
According to Newton's 3rd Law of Motion they are equal.
If the tree applies a force to the lorry (and it has to in order to stop it) then the lorry applies an equal and opposite force to the tree.
What then happens to the tree will depend on how it reacts to this force.

And you aren't thinking about momentum, you're thinking about force. If you are thinking about momentum you are thinking about conservation of momentum. Which just means that if the lorry suddenly stops. Then all the momentum is transferred into the driver, who with a much smaller mass, shoots forwards at a much higher velocity than the lorry was travelling at before the crash. (hence the damage done to the people in a car during a crash).
If the driver is not wearing a belt he continues to move at the same speed he had before the impact. This is the same speed as the lorry.

14. OK. Thanks for correcting me guys. I understand it better now.

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Updated: April 14, 2011
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