Exam 1 practice problems - Exam #1 practice problems...

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Unformatted text preview: Exam #1 practice problems Physics 203 1. You are standing next to the Physics Lecture Hall. Your friend has climbed up unto the roof and is sitting 6.00m above you with his legs dangling over the edge. His cell phone starts ringing (he left it with you before he climbed up). You toss him his cell but you toss it way too hard. It goes straight up passing your friend and reaches its apex (highest point) a full 3.00m above his head. He catches it on the way down and answers the phone. It's his mother, checking to make sure he's not doing anything he shouldn't be. a. Draw position, velocity, and acceleration graphs for the phone for the time interval that it was in flight. b. Predict how fast you tossed the phone (meaning, how fast it was traveling right after it left your hand). c. Predict how long the phone was in flight. d. What assumptions, if any, did you make in parts ac.? 2. A secretive group known as The Dharma Initiative has built a hidden underwater base just off a remote island in the South Pacific. This base is called The Looking Glass and its purpose is to jam all transmissions coming to or from the island. The people working in The Looking Glass need supplies regularly, which are dropped by boat from above. The base is 50 feet below the surface of the water. The supplies are packed in a waterproof steel box with a total weight of 200 pounds and are dropped from 10 feet above the surface of the water by a mechanical arm. Draw motion diagrams and force diagrams for the supplies from the moment they are dropped to the moment they arrive at The Looking Glass. Draw as many diagrams as you need to describe the situation in careful detail. 3. One of the problems astronauts face with spending long periods in space is adjusting back to earth gravity when they come home. Once we start traveling to other solar systems this will be an even more serious problem since those journeys will take years. One way to deal with this is to have the starship constantly accelerating at 9.81m s 2 . To the astronauts on board this will feel just like earth gravity. After 1 month of traveling, predict how fast this starship will be going, and how far it will have traveled. 1 4. A skydiver jumps out of an airplane at an altitude of 2000 meters and reaches terminal velocity ( 55.0 m s ) at an altitude of 1600 meters. She opens her parachute at an altitude of 800 meters and lands safely on the ground with a velocity of 6.11m s . a. Draw position, velocity, and acceleration graphs that describe the motion of the skydiver from the moment she steps out of the plane to the moment she lands on the ground. The values shown on the graphs do not need to be numerically precise, but their shapes do. b. Estimate how long it takes the skydiver to reach the ground. You will need to make several assumptions in order to be able to arrive at a numerical value. State each of the assumptions that you make and whether or not you think they are reasonable. 5. Coefficients of static friction are quantities that need to be determined experimentally. Suddenly you come up with a way to do this! You go into your kitchen and take out a wooden cutting board ( 50.0cm long with a mass of 1.20kg ) and a ceramic plate ( 10.0cm in radius with a mass of 0.40kg ). You put the cutting board down on the counter and place the plate at one end of it. You then begin lifting that end of the cutting board. The plate starts to We have not yet developed a power source that would have the ability to make a ship accelerate at this rate for such a long period of time. A nuclear fusion or some sort of matter/antimatter reactor would be able to accomplish this. We will likely see this sort of technology within our lifetimes. 1 slip when the cutting board makes a 27 angle with the counter. Use this information to determine the coefficient of static friction between the plate and the cutting board. 6. A skydiver's parachute is connected to him by 8 sturdy cables. When the parachute is deployed it causes the skydiver's speed to change from 90mph to 20mph in just 2.0s . a. Draw a motion diagram and a force diagram (or diagrams if you need more than one) for the skydiver from the moment he releases the parachute to just before he touches down on the ground. b. If the parachute is supposed to be safe for people up to 130kg what's the minimum force each cable must be able to withstand? c. What assumption(s) are you making in part b.? Do you think they are reasonable? If you were the one who had to design the parachute what would you do to take these assumptions into account? 7. You are studying for your second physics exam with your friends Clark and Lana. Clark says "So it seems to me that the net force on an object always points in the direction of the object's motion." Lana looks at him, unsure of whether to believe this. You say to Clark with a smile "What, do the laws of physics not apply to you or something? Here an experiment that disproves your hypothesis." Describe your experiment why it clearly disproves Clark's hypotheses. 8. You are designing an elevator for a new office building. The empty elevator has a mass of 700kg and needs to be able to handle between zero and 1500kg in passengers. In order for the passengers to feel comfortable the 2 magnitude of their acceleration must not exceed 2.00 m s . a. What is the maximum tension the elevator cable will experience during everyday operation? Start by drawing a motion diagram and a force diagram for the situation that causes the tension to be a maximum. b. What is the minimum tension the elevator cable will experience during everyday operation? Start by drawing a motion diagram and a force diagram for the situation that causes the tension to be a minimum. 9. You are pulling your 20.0kg suitcase (it has wheels) as you run through the airport at 3.00 m s . Because of your height, the strap you are pulling your suitcase with makes a 30 degree angle with the floor. a. Draw a force diagram for the suitcase. b. Make a numerical prediction of the force you will have to pull your suitcase with. If you have to estimate any additional physical quantities feel free to do so, but make sure you make reasonable estimates. 10. You (mass 70.0kg ) are moving into the second floor of a new apartment and have set up a ramp so you can roll your furniture up the stairs. The ramp has a 30.0 incline and thanks to its smooth surface and the welloiled wheels of the cart you are using, you have minimized the friction between the cart and the ramp so the coefficient of kinetic friction is approximately zero. You are at the top of the stairs on the level floor pulling the cart towards you at constant velocity with a rope. The rope is parallel to the incline. The bookcase and cart together have a mass of 40.0kg . What must the minimum coefficient of static friction between you and the floor be for you not to slip while you are pulling the cart up the stairs? For maximum credit you must include all force diagrams that are relevant for how you answered the question. 11. The idea of a train tunnel across the Atlantic Ocean has been around since 1895 when Jules Verne wrote about it. A modern version of a transatlantic tunnel would use what is called an "Archimedes bridge", which is an airtight tube tethered to the ocean floor that would float underwater at a depth of about 50.0m . The air pressure in the tube would be kept as low as possible, and magnetic levitation would be used to allow the trains to float above the tracks. If the train sped up all the way to the midpoint of the trip, then immediately started slowing down, the 5,000km trip from New York City to London would take just 1 hour. a. Predict the fastest speed the train would attain. Describe any assumptions you make. Do you think any of the assumptions you made are unreasonable? b. The passengers could feel some discomfort because they are continually speeding up or slowing down. To get an estimate of this, determine the ratio of the net force exerted on a passenger to the weight of that passenger. The smaller this ratio is, the more comfortable the passenger will be. 12. When an F/A18 Hornet (a U.S. Navy combat aircraft) has to land on an aircraft carrier it extends a hook to catch a cable that stretches across the landing deck of the ship. This cable must bring the plane to rest from its landing speed of 120mph in just 50.0m . What is the average acceleration that the pilot experiences? 13. A circus clown is shot nearly straight up out of a cannon, reaches a height of 25.0m , then falls back toward the ground landing safely in a thick airbag. a. Draw a motion diagram for the clown while he is in the air. b. Draw a free body diagram for the clown when he is at the top of his flight. c. Draw a motion diagram for the clown while he is in contact with the airbag. d. Draw a free body diagram for the clown while he is slowing down inside the airbag. e. How can you check to see if your motion diagrams and free body diagrams are consistent? 14. The graph shows the motion of a person riding their bicycle along a straight path. a. How far does the person move in 5.0s ? b. What is the slope of the line? c. What is the person's velocity? d. Write the equation for the line, first using only symbols, and then using only numbers except for x and t . 15. You have been asked to design an Olympic size swimming pool with a 3 meter springboard. (A springboard is a diving board that is flexible so divers can use it to launch themselves upwards at the beginning of the dive. This particular spring board is 3 meters above the water will launch a diver at most 1 meter upward.) Water does a good job of slowing the diver down safely so they don't hit the bottom of the pool, and will cause the diver to slow down at a minimum rate of 12m/s each second. a. How deep does the pool have to be so that divers will not hit the bottom? b. What assumptions did you make in the method you used? Will any of these assumptions cause you to underestimate how deep the pool should be? (That would make it dangerous for divers.) 16. Draw motion diagrams and force diagrams for the diver in the previous problem. Draw as many as you need so that the entire motion of the diver has been represented, from when they leave the board to when they reach their maximum depth underwater. 17. A daredevil (mass 80 kg) jumps out of the 5 story of a burning building (20m above the ground.) A 3m thick air bag cushions his fall. Estimate the average force the air bag exerts on the daredevil while he is crashing into it. Hint: First determine how fast the daredevil will be traveling when he first comes into contact with the air bag. 18. A car is traveling along a straight, level road at a constant speed of 18m/s. Right at the moment it reaches the base of a hill the ignition fails causing the engine to shut off. The driver is hoping to coast up and over the hill since he knows there is a gas station on the other side. The hill is 16m high and the car will have to coast a total of 150m if it's going to reach the top of the hill. a. Decide if the car will make it over the top of the hill. Justify your decision quantitatively. b. Describe the assumptions you made in making the decision. In what way does making these assumptions affect the decision? c. Choose one of the assumptions. In as much mathematical detail as you can show how you would incorporate the piece of physics you decided to leave out when you made the assumption. 19. Top fuel dragsters have the largest acceleration of any manned vehicle on Earth: Larger than the space shuttle on takeoff, larger than a catapult assisted F18 fighter jet launched from an aircraft carrier. While testing a new engine design, a dragster completes a quarter mile (402m) time trial in 4.45 s. a. Assuming the dragster accelerates at a constant rate, estimate its acceleration. b. Estimate how fast the dragster will be traveling in mph when it crosses the finish line. c. Imagine that a sports car traveling at a constant 200mph crosses the start line right when the dragster starts accelerating from rest for its 4th time trial. Predict who will win this very unfair sounding race. d. Sketch position, velocity, and acceleration graphs for the dragster and the sports car. Show the two vehicles on the same graphs. 20. Three tugboats are using long steel cables to an aircraft carrier out of a repair dock. Each of these tugboats can exert a 150,000N pulling force. The tugboats are all sidebyside with 40m between them, with the one in the middle directly in front of the aircraft carrier. The middle tugboat is directly in front of the aircraft carrier and 200m from it. All three cables are attached to a common point at the front of the aircraft carrier. It takes 15 minutes to get the aircraft carrier up to the desired speed of 10m/s. a. Estimate the mass of the aircraft carrier. b. Describe the assumptions you made in making your estimate. 21. A car is traveling at 55mph northbound on Route 1. 100m ahead a traffic light turns yellow. As soon as the driver notices this he puts his foot on the brake pedal and begins slowing down. th a. Determine how long it takes for the car to come to rest. If your method makes any assumptions describe what they are. b. Draw position vs. time, velocity vs. time, and acceleration vs. time graphs for the entire motion of the car. (These are graphs, not sketches, so make them as precise as you can. Include all relevant numerical values, labels, etc.) ...
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