Question

1. Describe the universal gravitational law.

Answer 1

Answer:

1. The law of universal gravitation is $F = \frac{G*m1*m2}{r^{2}}$, where F=force, G=gravitational constant, m=mass, r=radius. It's an inverse square law, because there's a squared term in the denominator. It's really neat because it's basically the same thing as Coulomb's law ($F = \frac{k*q1*q2}{d^{2}}$) but just with big things instead of small ones!

2. Ptolemy was a Greek mathematician who believed in a geocentric model, or that the earth was the center of the universe and the sun revolved around it. Copernicus believed in a heliocentric model, which is exactly the opposite. Of course we now agree with Copernicus. Both scientists used extensive proofs and logic to come to their conclusions, but ultimately Copernicus was correct.

3. The first image, Path A, shows how the ball will fly. This is because of Newton's laws: the object will keep going in the direction it was last going. The force is not circular; the force is basically tangent to the circle at every point. Just try doing this with your bike (I do this in my driveway) by spinning in circles, then just stopping: you will go along Path A. Also, this is the centripetal force, which says that the force is towards the inside; this causes the ball to go outwards when you let go.

Answer 2

Answer:

1. Discovered by Sir Isaac Newton, this law states that every object in the universe that has mass attracts every other object in the universe that has mass. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. When applying this to a situation with two objects, the object with the smaller mass will do most of the moving because the other object has too much inertia to move any noticeable amount.

2. Without advanced technology like we have today, Ptolemy and Copernicus tried to best explain the model of the universe through observation. Ptolemy’s model came first and placed a stationary earth at the center of the model. Everything else moved in respect to earth. This was widely accepted since it seemed like earth wasn’t moving. Ptolemy stated that the planetary bodies moved around earth in circular paths. However, this wasn’t always witnessed through observation. He adjusted his model to state that some planets must be moving in secondary orbits.

Copernicus put a rotating earth in a sun-centered model. The rotation of earth was able to account for the rising and setting of stars. The orbital motion of the earth and moon also accounted for the motion of the sun and moon with respect to the stars. This was easier to understand but encountered scrutiny due to its differences from religious teachings.

One big difference between the approaches in the two is that Copernicus didn’t try to adjust his model to match what was going on; he used observations to develop the model. In addition, one common trend in science is that the simplest explanation is usually most accurate or closer to accurate. Copernicus’ model was more straightforward; Ptolemy’s was more complex.

3. Acceleration in a circle is toward the center of the circle, while velocity is always a straight line that's tangent to the circle. Thus, when the boy lets go of the rope, the centripetal force (acceleration) toward the center of the circle disappears. The ball then follows the straight path, tangent to the circle, and follows Path A.

Explanation:

Straight from Penn Foster