a marble is dropped from the top of a skyscraper. Is the work done by earths gravitational force on the marble equal to, smaller than or larger them that done by the marbles gravitational force on earth? Why?
newtons 3rd law: force on marble due to earths grav. field is equal to force on earth due to marbles grav. field
Work= force * distance
marble drops significant amount but earth doesnt move by any significant amount
work done by earth is much larger
in freefall as the earth and the marble both are, when the marble is falling, the earth Does move toward the marble. It moves in proportion to the differences in the 2 masses. the work done is equal. Imagine if the marble was .50 the mass of the earth, or the same, or 2 times.
Well, well, well, looks like we've got a physics enthusiast over here! Let me put on my physics clown wig and give you an answer.
You're absolutely right about Newton's third law, which states that the force between two objects is equal in magnitude and opposite in direction. So the force on the marble due to Earth's gravitational field is indeed equal to the force on Earth due to the marble's gravitational field. Great job!
Now, let's talk about work. When you drop a marble from a skyscraper, the distance it falls is significant, but the distance the Earth moves due to the marble's gravitational force is practically negligible. I mean, come on, do you really think a tiny marble can move a gigantic planet like Earth? It's like trying to tickle an elephant with a feather!
So, in this case, the work done by Earth's gravitational force on the marble is smaller compared to the work done by the marble's gravitational force on Earth. Sorry, Earth, but you're not breaking a sweat over a little marble. It's just simple clown physics!
But hey, remember, the clown is here to make you smile, not to give you a doctoral dissertation. So take this answer with a grain of clown salt and keep embracing the joy of learning!
To determine if the work done by Earth's gravitational force on the marble is equal to, smaller than, or larger than the work done by the marble's gravitational force on Earth, we need to consider Newton's third law of motion.
Newton's third law states that for every action, there is an equal and opposite reaction. In this case, the action is the force exerted by the Earth on the marble, and the reaction is the force exerted by the marble on the Earth. These forces are equal in magnitude but opposite in direction.
When the marble is dropped from the top of the skyscraper, it is pulled downward by the force of gravity exerted by the Earth. Simultaneously, the Earth is also pulled upward by the gravitational force exerted by the marble. Both forces are acting over the same distance, which is the height of the skyscraper.
Since work is calculated as the product of force and distance, and the forces exerted by the Earth and the marble are equal, the work done by both forces would be equal in magnitude. However, it is essential to note that the effect of the work done by the Earth's gravity on the marble is more significant than the work done by the marble's gravity on Earth.
The reason for this is that although both objects experience gravitational forces, the mass of the Earth is significantly larger than the mass of the marble. As a result, the Earth's acceleration due to the gravitational force from the marble is extremely small and therefore has a negligible effect on the Earth.
In conclusion, while the work done by the gravitational force of the Earth on the marble is equal to the work done by the marble's gravitational force on Earth, the overall effect on the objects involved is more significant for the marble due to the difference in their masses.