Question

Jessica's weight is 540 newtons. According to the Third Law, if the Earth pulls on Jessica with a force of 540 N, then Jessica pulls on the Earth with a force of 540 newtons that acts in the opposite direction. However, if Jessica stumbles while rollerblading, she will fall down to the ground. Explain why this happens.

Answer 1

Gah, this really messes with your mind, doesn't it?

Think of the forces in terms of what they represent. A force is something that induces an acceleration in an object. However, the difference in this case is defining what is present in the equations.

Both forces are 540 N. We must look at the equation that governs forces in order to see why she falls down.

F = MA defines force as a mass times an acceleration.
Therefore:
Fj = 540 N
Fe = 540 N

Since both forces are equal, let's equate them.

Fj = Fe --> Mj * Aj = Me * Ae

Now we are not given exact values for this, but we can use some averages so I can show this more clearly.

The average human weight is about 60 kg, give or take. The mass of the Earth is on the order of 10^24 kg. We also know that Jessica's acceleration is by Earth's gravity, which is 9.8 m/s^2.

Plugging these values into our equation looks like this:

60 * 9.8 = (10^24) * Ae --> 588 = (10^24) * Ae --> Ae = 5.88 x 10^-22 m/s^2

Notice how the acceleration of the Earth Ae is really really tiny!! This is the reason Jessica falls down to the Earth's surface. Jessica accelerates towards the Earth much faster than the Earth accelerates towards Jessica. Therefore, Jessica will "fall". The Earth is technically moving upwards to meet Jessica as she falls, but it is such a severely negligible amount that it's completely insignificant to discuss.

Hope this helps to clarify a little bit. When dealing with forces, consider the defining equation and see the major differences between both sides!

Just because forces are equal DOES NOT mean that their accelerations are the same! Acceleration due to force is dependent on the mass of the object too!