# Newtons 3rd Law - AAMC 4 Item 40

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#### LaughingMan

##### Avoid Arrogance
10+ Year Member
Hey All,

Having a hard time conceptually understanding this.

A continent of mass m collides with a continent of mass m/2 that is initially at rest. During the collision the more massive continent is found to exert a force F on the less massive continent, causing the smaller continent to accelerate. At the same time, the less massive continent exerts a force on the larger continent of magnitude:

A. F/2
B. F
C 2F
D 0

I choose A, the answer is B.
If the smaller continent is exerting the same F, then wouldn't that make it

F= MA
F (Larger Continent) - F(Smaller Continent) = (M)(A) **Now since the continent is accelerating, the two opposing forces can't cancel each other out? Thus I thought to myself, the smaller continents force must be smaller so as we have SOME acceleration?

Where am I going wrong here?

Edit: Should also add, the context of the passage, leads me to believe the collision is INELASTIC.

Last edited:

#### milski

##### 1K member
10+ Year Member
No, the forces are applied on different bodies - you don't need to add or subtract them. The large continent exerts a force on the small one F and the you have F=masmall. According to the 3rd law the small continent exerts equal in size and opposite in direction force on the large continent, which will get F=Malarge. The large continent will also accelerate according to that equation.

#### BerkReviewTeach

##### Company Rep for now-defunct Course & Bad Singer
Vendor
15+ Year Member
Hey All,

Having a hard time conceptually understanding this.

A continent of mass m collides with a continent of mass m/2 that is initially at rest. During the collision the more massive continent is found to exert a force F on the less massive continent, causing the smaller continent to accelerate. At the same time, the less massive continent exerts a force on the larger continent of magnitude:

A. F/2
B. F
C 2F
D 0

I choose A, the answer is B.
If the smaller continent is exerting the same F, then wouldn't that make it

F= MA
F (Larger Continent) - F(Smaller Continent) = (M)(A) **Now since the continent is accelerating, the two opposing forces can't cancel each other out? Thus I thought to myself, the smaller continents force must be smaller so as we have SOME acceleration?

Where am I going wrong here?

Edit: Should also add, the context of the passage, leads me to believe the collision is INELASTIC.

Because the objects stuck together after the collision, it is inelastic. But that is irrelevant.

If you happen to have book 1 laying around, this is case 3 on pages 183-184. I like milski's way of looking at it as "equal and opposite forces" during the collision, as that's what the test writer's tone suggests they are asking about. But if that is not your first inkling, then you can consider the impulse (as presented in case 3) where each object experiences an equal magnitude of impulse, but in opposite directions. What one object loses in momentum the other one must gain. Because J = Fimpact x tcollision and the collision time is the same for both objects, the two objects must experience equal, but opposite forces, during collision.

The last way to look at it is from a calculation perspective. The velocity of the system after collision = 2/3 velocity before collision (passage 1 on page 202 shows the math). So, Object I has mass = m and a [delta]v = -0.333 viniitial. Meanwhile, Object II has mass = m/2 and a [delta]v = +0.667 viniitial. If you consider ma for either system, you'll get the same numerical value (0.333mviniitial/time), but in opposite directions. That is a good amount of math to simply get to where milski took us by simply consiering the Newton's third law.

And what's wrong with your initial perspective is that you are focusing on just the smaller, initially stationary object when you are thinking of ma. You must also consider that the incident object slows down, so the net acceleration of the entire system is 0, which means there is no external force acting on the system.

#### Yessi211

##### New Member
10+ Year Member
The first thing I see that you did wrong was writing the forces together in the same equation. They are acting on different objects and should not be put in the same equation. This probably tells me that you're forgetting to draw out your force diagrams (which are extremely helpful if you're new to physics problems involving forces!).

According to Newton's third law, the larger continent exerts a force of equal magnitude and opposite direction on the smaller continent. What differs is the "affect" of these forces. Because the smaller continent has half of the mass of the larger one, it will accelerate faster as a result of the applied force. The magnitude of the forces are the same, the affects are different!

Hope this helps