. A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. (See below.) Prove that the body leaves the sphere when 0 = cos¹ (2/3). R 0

Three billiard balls, the two-ball, the four-ball, and the eight-ball, are arranged on a pool table as shown in Figure P7.26. Given the coordinate system shown and that the mass of each ball is 0.150 kg, determine the gravitational force on the eight-ball due to the other two balls.

Saturns ring system forms a relatively thin, circular disk in the equatorial plane of the planet. The inner radius of the ring system is approximately 92,000 km from the center of the planet, and the outer edge is about 137,000 km from the center of the planet. The mass of Saturn itself is 5.68 1026 kg. a. What is the period of a particle in the outer edge compared with the period of a particle in the inner edge? b. How long does it take a particle in the inner edge to move once around Saturn? c. While this inner-edge particle is completing one orbit abound Saturn, how far around Saturn does a particle on the outer edge move?

A system consists of three particles, each of mass 5.00 g, located at the corners of an equilateral triangle with sides of 30.0 cm. (a) Calculate the gravitational potential energy of the system. (b) Assume the particles are released simultaneously. Describe the subsequent motion of each. Will any collisions take place? Explain.

Chanur Part 11 of 11 - Analyze Now Chandra and Darcel decide to try a problem. Suppose that the height of the incline is h = 15.3 m. Find the speed at the bottom for each of the following objects. X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a digit accuracy to minimize roundoff error. m/s m/s m/s m/s solid sphere spherical shell hoop cylinder In a race, which object would win? O solid sphere O spherical shell O hoop O cylinder O tie Submit Skip (you cannot come back) H t of MR², it is poss Search HH

P1 A pendulum of length L with a bob of mass m is released from the vertical position without initial speed. Under the suspension point, a nail is fixed at a distance of L – x. The thread of the pendulum gets stuck in the nail during its motion so that the bob starts to move on a circular path of radius x after it has reached its lowest position. L m a) At most how large should x be if the bob executes a complete circle? b) If x = L/3, calculate the tension in the thread when the bob reaches its highest po- sition during the motion after the thread gets stuck in the nail.

Example questions Sad ball Наpрy ball 1. Students are given two spherical balls made of different materials, but of identical mass and diameter to experiment with. Each ball is dropped from an initial height, ho. The "sad ball" comes to rest without visibly bouncing when it strikes the tabletop. The "happy ball" bounces up to a final height h, where h < ho- A fellow student wants to use one of the balls in a carnival game where cups are knocked over by a thrown ball. Which ball should they use, happy or sad? In a clear, coherent, paragraph-length response that may also contain figures and/or equations, explain what physics principles explain why the happy ball bounces higher off of the tabletop and explain which ball makes the better choice as a projectile in the carnival game. A Answer the Question Basic Physics Cite Information Draw it all together

60 Look at the diagram. a i Calculate the minimum speed v the ball must have in order to make it to position B. ii What speed will the mass have at B? b Given that v= 12.0 ms¹, calculate the speed at A and B. 4.0 m A 2.0 m B

Please answer Question 8 parts b-d

A planet is observed to be in an elliptical orbit around the sun as shown below. Which of the following quantities, if remain constant over the time it takes to complete one orbit? any, planet Sun (a) force exerted by the sun on the planet F (b) momentum p (c) angular momentum L (d) orbital speed v (e) kinetic energy K (f) potential energy U (g) total energy E Explain each of your choices and state any assumptions you made.