5. (25 points) Cartman, Kyle, and Kenny have discovered a big hole at the top of a mountain near South Park They've built a setup to allow them to lower Kenny down into the hole, to see what's down there (see the picture). Kenny is in a cardboard box (they cut a hole in the side so he can see out), with a pulley attached. A rope goes over the three pulleys as shown, with Cartman and Kyle holding onto the two ends of the rope, to try to slowly lower Kenny into the hole. Cartman is sitting on his Big Wheel bike on the 30 incline shown, pressing the brakes, to keep the wheels from rolling. The coefficient of static friction between him and the ground is large enough that he's staying where he is not being dragged up the incline. Kyle is sitting on his butt on a 60° incline, being dragged up the incline. The coefficient of friction between Kyle's pants and the ground is 0.3. Cartman and Kyle have masses of 40 and 30 kg respectively (Cartman's Big Wheel has a mass of 6 kg). Kenny and the box he is in together have a mass of 150 kg. What is the minimum coefficient of static friction between Cartman's tires and the ground so that he won't slide while Kenny is being lowered into the well? 30° 60° 4. (20 points) Planet Kerbin has a mass of 9.0x10² kg, and a radius of 700,000 meters, making it smaller than our moon. Recall that Newton's Law of Gravity says two bodies exert an attractive gravitational force on each other equal to F = Gm, m where r is the distance between the centers of mass of the two objects in question. The Gravitational constant G is 6.674x10-11 m3 a. Assume for the moment that planet Kerbin is not spinning. If you dropped a 100 gram apple from a little ways above the surface of the planet, how fast would it accelerate towards the planet? (in other words, what is the acceleration due to gravity) b. Now let's say planet Kerbin is spinning quite fast. A day on Kerbin is only 2 hours long (2 of our Earth hours). If you are standing on Kerbin's equator, and drop an apple, how fast will it accelerate towards the planet when you account for the planet's rotation? (this involves the answer to part a, but also recognizing that the surface of the planet itself is accelerating due to its rotation, and figuring out how fast the apple would be accelerating relative to the surface of the planet) c. What would the centripetal acceleration be for something located at 30° Latitude (30° above the equator)? For long answer problems SHOW ALL OF YOUR WORK CLEARLY. That means draw nice clear FBDs and explicitly write out Newton's 2nd Law for each object. That is far more important than getting all of the algebra right. 3. (15 points) You are training your dog, “Professor Fluffy-pants", to pull dog sleds. To help build his strength, you have loaded weight onto two sleds for him to practice pulling, as shown below. Sled A has a total mass of 100 kg and sled B has a total mass of 80 kg (the total mass means the combined mass of the sled plus the weight you have added). You have attached a rope (rope 1) between sleds A and B as shown, and tied another rope from sled B to Professor Fluffy-pants. Rope 1 is some cheap rope you found on the side of the road, and it will break if the tension reaches 400 Newtons. a.) What is the maximum acceleration sled A can have before rope 1 breaks? Assume the coefficient of friction between the sled and the snow is 0.3. b.) What is the hardest that Professor Fluffy-pants can pull on rope 2 without breaking rope 1? A B 100 kg 180 kg 2
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