1. A car with a mass of 1,500 kilograms is moving around a circular curve at a uniform velocity of 16 m/s. The curve has a radius of 100 meters. What's the centripetal force on the car?

2. A car with a mass of 1,200 kg is moving around a circular curve at a uniform velocity of 20 m/s. The centripetal force on the car is 6,000 N. What's the radius of the curve?

Write your answers using 1-2 paragraphs.

3. Describe the universal gravitational law.

4. Evaluate the techniques and models used by Ptolemy and Copernicus to explain the setup of the universe.

Answers

1) 3,840 N

2) 80 m

Explanations

Centripetal force is the force that maintenance objects that are moving in a circular motion.

F = mv²/r

= (1500 * 16²) / 100

= (1500*256) / 100

= 384000/100

= 3,840 N

2) F = (mv²) / r

6000 N = (1200 * 20²) / r

r = (1200 * 400) / 6000

= 480,000/6000

= 80 m

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.

4. 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 was not moving. Ptolemy stated that the planetary bodies moved around the 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.