Question

tonHint: The assumption was not "it's moving in a circle."1 2. Claiming that a particle is moving in a circle with a constant radius is logically/mathematically equiv- 3. Consider a particle moving in a cirele of radius R. How is it posible for the particle to experience an 4. After deriving the formula for centripetal acceleration, we were inspired by Newton's d Law to alent to two other claims. State at least one of those claims. acceleration when its speed is constant? multiply by the mass in order to get the centripetal force. However, "centripetal force" is merely a label that can be added onto other forces. What condition must centripetal force? a force satisfy in order to be called a 5. Consider a car driving at a constant speed around a perfectly circular race-track. What foree plays the role of the centripetal force? [Hint: Ignore air friction.] 6. When we examined the work done by a centripetal force, we saw that it was O J. How is this possible for a non-zero force and a non-zero displacement? Hubble Space Telescope orbits the Earth at an altitude of about 568 kilometers. Since it's been n orbit since the year 1990, we may assume that it's in a stable orbit. How fast must it be going? 8. How fast is a person on the equator moving around the center of the Earth? 9. What is the mass of the Sun? Note: Do not use Kepler's 3"d Law to solve this.) 10. Imagine standing on the sidewalk by the Empire State Building. It has a mass of approximately 3.31 x 108 kg and technically exerts a gravitational pull on you. Determine what percentage of the Earth's gravitational pull on you is the gravitational pull you feel from the Empire State Building. 11. Consider 2 asteroids in interstellar space, with no other significant mass anywhere near them. Asteroid A is 1000 times as massive as Asteroid B, and yet Newton's 3rd Law of Motion and the formula for Newton's Law of Universal Gravitation ensure that they will each feel the same net force magnitude of gravitational attraction from one another. However, Asteroid B will be observed to move toward Asteroid A, and Asteroid A will barely move at all. How can this be if they feel the same net force?

Answer 1

2. Statement particle moving in a circle with a constant radius can be state as particle is moving in a track of circumference $2\pi R$ (R is radius of circle) or particle is moving on a circle of constant planar area $\pi R^{2}$ .

3. In uniform circular motion speed is constant but direction of particle motion change. Hence velocity change (velocity is vector quantity). Hence acceleration (rate of change of velocity) also change.

4. Requirement for centripetal force is circular motion. Uniform circular motion has acceleration and hence inward force which is centripetal force.

5. Friction force acting upon wheels of the car and road provides centripetal force required for circular motion.