# Newton's Third Law Questions

1. Oct 10, 2011

### domtar

1. Tug Of War: Person A is bigger and stronger than Person B, and chooses to neither pull on the rope, or allows Person B to pull Person A forwards. Assume that Person A's force is in the positive direction, graph both forces on one set of axis.

Approach: For Person A to neither pull or allow to be pulled, I'm assuming that the forces must be balanced and be in equilibrium. Does this mean that the force vs time graph would be a constant, straight horizontal line? That is my answer, just wondering if it was correct.

2. A 70.0kg astronaut pushes to the left on a spacecraft with a force F in "gravity-free" space. The spacecraft has a total mass of 1.0 x 10^4 kg. During the push, the astronaut accelerates to the right with an acceleration of 0.36m/s/s. Determine the magnitude and direction of the acceleration of the spacecraft.

Approach: This is an action-reaction pair, so both forces must be equal. Therefore the force of the spacecraft moving to the left must equal the force of the astronaut when he moves to the right (after he pushes the spacecraft). I began by using F=m/a, where m=70.0kg and a=0.36m/s/s, and my answer was 194.44N. This is the force of the astronaut moving to the right, so the force of the spacecraft moving to the left would be a=F/m, where F=194.44m/s/s, and m=1.0 x 10^4, and my answer was 0.0194m/s/s.

I'm assuming that this means that the acceleration of the spacecraft is -0.0194m/s/s since it's moving to the left. I'm very skeptical about my answers though so I was just wondering if the approach and calculations were correct? I appreciate any help and advice, thanks.

2. Oct 10, 2011

### lightgrav

The first scenario sounds like the Big guy moved forward with zero Force applied to him.

the massive spacecraft didn't accelerate quickly; that ought to make sense.

3. Oct 10, 2011

### domtar

Thanks for the reply, but how does the big guy move with zero force applied to him?

4. Oct 10, 2011

### lightgrav

How can he NOT pull on the rope, if the little guy tries to pull on it?
Only by moving forward under his own power.

5. Oct 10, 2011

### domtar

Oh I see, thanks a lot!