Question

Newton's laws of motion work well for ordinary situations on earth. However, these laws of motion do not work for all cases. Under what condition will Newton's second law not work? A) For objects at extremely low speeds. B) for objects that are extremely small. C) For objects at extremely fast speeds. D) For objects that are very far away from earth.

Answer 1

Answer:

C: for objects at extremely fast speeds.

Explanation:

Newton's second law does not hold for extremely fast speeds, because then relativistic effects come into play, where Einstein's theory of special relativity is a more correct description.

The reason why F=ma does not hold for fast speeds is that, as an object moves faster and faster, the proportional relationship between force and acceleration does not hold. As an object moves faster and faster, it becomes harder and harder (requires more force) to accelerate it. because it gains mass as a virtue of its velocity (what's called relativistic mass).

For relativistic speeds, the correct modification of Newtons second law is:

$F=\frac{dp}{dt}$

where $p$ is the relativistic momentum:

$p=\frac{mv}{\sqrt{1-\frac{v^2}{c^3} } }$