## Problem 1: Keith Hernandezâ Brownstone

ŵŵŴ Â ÂÂÂ Â ŵŹ ŶŴŵŶPlease answer the question in the space provided below. Partial credit will begiven to incomplete or incorrect final answers. Each question is worth 25points.Problem 1: Keith Hernandezâ BrownstoneYou are asked to help a new friend move out into his new house despite thefact that you have only known him a week. Begrudgingly, you accept.The first item is a 100 kg piano which hauled upward by a rope and pulleysystem to the second floor foyer.1.1. If the piano does not accelerate, what is the tension force, T, applied tothe piano?1.2 How much work is required to pull the piano a distance 5.0m up to thesecond floor?A second, very pumped up, friend decides to help pull an additional 5.0 m.The piano accelerates at a rate of 0.2 g.1.3 What is the net work done on the piano?1.4 What is the speed of the piano after it travels 5m?Problem 2: Satellite of LoveBobby and Paulette have unveiled their new ride for the 2012 summer reopening of Adventureland. It is the worldâs tallest, recycled roller coaster. Itsloop has a radius 20m connected to a track which is advertised asfrictionless. The 850kg cart is released from rest atop of hill of height, 80m.BA2.1 What is total energy of the cart?2.2 What is the cart speed at A? B?2.3 If a second loop is constructed next to the first, what is the maximumradius such that the cart would not fall off?2.4 To slow the cart after its travel around the loop the loop, a sticky,1000kg mass is placed on the track. Upon collision, the cart and mass sticktogether. By how much does the cart slow down?Problem 3: Missing MassConsider a star with mass equal to our sun, ŵ Horbiting the center of the galaxy with mass Hdistance of J ŷ ŵ ŵŴ#" ˞˚Jˮ˥ ˙ź źŻ ŵŴ##˞ŷ ŷ ŵŴ’ H,#ŵŴ Hat aźŷŻ% ŵŴ% ˭ HŵŴ$& ˫˧ ,3.1 What is the gravitational force between the star and galaxy?źŴ3.2 Assume the orbit of the star about the galactic center is circular,Calculate the speed at which the star orbits the galaxy. Hint: the motion iscircular.3.3. If astronomers discover that the speed of the star is twice as large asthey calculate, how massive must the galaxy be to account for the largespeed? (hint: there is a quick way to solve his and a long way)Problem 4: Apples & Tangerines4.1 A car can skid off the road if its speed exceeds the maximum speed atwhich the car remains static with respect to the road.For a flat road, label the forces that act on the car and identify the forcewhich keeps the car on the road. What happens when the car begins toskid?4,2 Race cars can easily exceed the minimum turning speed between roadand tire. What corrective measure can be used to increase the speed at whicha car can safely make a turn without skidding?4.3 Consider the orbit of a planet around the Sun as shown below:Using Keplerâs 2nd Law, contrast the motion of the planet between points Cto D and A to B in terms of their speed.For a highly elliptical orbit, will a planet have extreme seasonal differences,no seasons, or mild seasonal differences? Explain.4.3 What is a black hole?Label the regions of the black hole below and indicate whether the escapevelocity of an object is greater than, equal to, or less than the speed of lightin the region inside and outside the boundaryList two effects a black hole has on an object as it falls in.

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