Forces Context Rich Problems

SPH4U: Forces – Context Rich Problems

I do not have answers to these problems, and I haven’t thought about how to solve them. They are all fairly challenging and fair game for a test question. Work with friends on them, explain your solutions and convince yourselves that you understand the problems. I can’t tell you if you are right - I just don’t know!

1. Tension, Weight, Friction: You are taking advantage of an early snow to go sledding. After a long afternoon of going up and down hills with your sled, you decide it is time to go home. You are thankful that you can pull your sled without climbing any more hills. As you are walking home, dragging the sled behind you by a rope fastened to the front of the sled, you wonder what the coefficient of friction of the snow on the sled is. You estimate that you are pulling on the rope with a 2 pound force, that the sled weighs 10 pounds, and that the rope makes an angle of 25 degrees to the level ground

2. Tension, Weight: You are part of a team to help design the atrium of a new building. Your boss, the manager of the project, wants to suspend a 20-lb sculpture high over the room by hanging it from the ceiling using thin, clear fishing line (string) so that it will be difficult to see how the sculpture is held up. The only place to fasten the fishing line is to a wooden beam which runs around the edge of the room at the ceiling. The fishing line that she wants to use will hold 20 lbs. (20-lb test) so she suggests attaching two lines to the sculpture to be safe. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has one line making an angle of 20o with the ceiling and the other line making an angle of 40o with the ceiling. She knows you took physics, so she asks you if her design can work.

3. Weight, Normal: While driving in the mountains, you notice that when the freeway goes steeply down hill, there are emergency exits every few kilometers. These emergency exits are straight dirt ramps which leave the freeway and are sloped uphill. They are designed to stop trucks and cars that lose their breaks on the downhill stretches of the freeway even if the road is covered in ice. You wonder at what angle from the horizontal an emergency exit should rise to stop a 25 tonne truck going 110 km/h up a ramp 100 metres long, even if the frictional force of the road surface is negligible

4. Weight, Normal, Friction: You are passing a construction site on the way to physics class, and stop to watch for awhile. The construction workers appear to be going on coffee break, and have left a large concrete block resting at the top of a wooden ramp. As soon as their backs are turned, the block begins to slide down the ramp. You quickly clock the time for the block to reach the bottom of the ramp at 10 seconds. You wonder how long the ramp is. You estimate that the ramp is at an angle of about 20o to the horizontal. In your physics book you find that the coefficient of kinetic friction between concrete and wood is 0.35

5. Weight, Normal, Tension, Friction: Finally you are leaving Toronto to get a few days of March Break, but your car breaks down in the middle of nowhere. A tow truck weighing 4000 lbs. comes along and agrees to tow your car, which weighs 2000 lbs., to the nearest town. The driver of the truck attaches his cable to your car at an angle of 20o to the horizontal. He tells you that his cable has a strength of 500 lbs. He plans to take 10 seconds to tow your car at a constant acceleration from rest in a straight line along the flat road until he reaches the maximum speed limit of 80 km/h. Can the driver carry out his plan? You assume that rolling friction behaves like kinetic friction, and the coefficient of rolling friction between your tires and the road is 0.10.

6. Weight, Normal, Circular: Just before finals you decide to visit an amusement park set up in the Metrodome. Since it is a weekend, you invite your favorite niece along. She loves to ride on a Ferris wheel, and there is one at the amusement park. The Ferris wheel has seats on the rim of a circle with a radius of 25 m. The Ferris wheel rotates at a constant speed and makes one complete revolution every 20 seconds. While you wait, your niece who has a mass of 42 kg, rides the Ferris wheel. To kill time you decide to calculate the total force (both magnitude and direction) on her when she is one quarter revolution past the highest point. Because the Ferris wheel can be run at different speeds, you also decide to make a graph which gives the magnitude of the force on her at that point as a function of the period of the Ferris wheel.

7. Weight, Normal, Circular: While relaxing from studying physics, you watch some TV. While flipping through channels you see a circus show in which a woman drives a motorcycle around the inside of a vertical ring. You determine that she goes around at a constant speed and that it takes her 4.0 seconds to get around when she is going her slowest. If she is going at the minimum speed for this stunt to work, the motorcycle is just barely touching the ring when she is upside down at the top. At that point she is in free fall so her acceleration is just g. She just makes it around without falling off the ring but what if she made a mistake and her motorcycle fell off at the top? How high up is she?

8. Weight, Normal, Friction, Circular: The producer of the last film you worked on was so impressed with the way you handled a helicopter scene that she hired you again as technical advisor for a new "James Bond" film. The scene calls for 007 to chase a villain onto a merry-go-round. An accomplice starts the merry-go-round rotating in an effort to toss 007 (played in this new version by Billy Crystal) off into an adjacent pool filled with hungry sharks. You must determine a safe rate of rotation such that the stunt man (you didn't think Billy would do his own stunts did you?) will not fly off the merry-goround and into the shark-infested pool. (Actually they are mechanical sharks, but the audience doesn't know that.) You measure the diameter of the merry-go-round as 50 meters. You determine that the coefficient of static friction between 007's shoes and the merry-go-round surface is 0.7 and the coefficient of kinetic friction is 0.5.

9. Weight, Normal, Friction, Circular: On a trip through Florida, you find yourself driving in your 3000-lb car along a flat level road at 80 km/h. The road makes a turn which you take without changing your speed. The curve is approximately an arc of a circle with a radius of 30 meters. You notice that the curve is flat and level with no sign of banking. There are no warning signs but you wonder if it would be safe to try to go 80 km/h around the curve in the rain when the wet surface has a lower coefficient of friction. What is the minimum coefficient of static friction between the road and your car's tires which will allow your car to make the turn?

10. Gravitational, Circular: You are still a consultant for the new Star Trek TV series. You were hired to make sure that any science on the show is correct. In this episode, the crew of the Enterprise discovers an abandoned space station in deep space far from any stars. This station, which was built by Earth in the 21st century, is a large wheel-like structure where people live and work in the rim. In order to create "artificial gravity," the space station rotates on its axis. The special effects department wants to know at what rate a space station 200 meters in diameter would have to rotate to create "gravity" equal to 0.7 that of Earth.

11. Gravitational, Circular: You did so well in your physics course that you decided to try to get a summer job working in a physics laboratory at the University. You got the job as a student lab assistant in a research group investigating the ozone depletion at the Earth's poles. This group is planning to put an atmospheric measuring device in a satellite which will pass over both poles. To collect samples of the upper atmosphere, the satellite will be in a circular orbit 320 km above the surface of the Earth where g is 95% of its value on the Earth's surface. To adjust the instruments for the proper data taking rate, you need to calculate how many times per day the device will sample the atmosphere over the South pole. Using the inside cover of your trusty Physics text you find that the radius of the Earth is 6.38 x 103 km and the mass of the Earth is 5.98 x 1024 kg.

12. Weight, Lift, Circular: You are reading an article about the aesthetics of airplane design. One example in the article is a beautiful new design for commercial airliners. You are worried that this light wing structure might not be strong enough to be safe. The article explains that an airplane can fly because the air exerts a force, called "lift," on the wings such that the lift is always perpendicular to the wing surface. For level flying, the wings are horizontal. To turn , the pilot "banks" the plane so that the wings are oriented at an angle to the horizontal. This causes the plane to have a trajectory which is a horizontal circle. The specifications of the 5.00 x 104 kg plane require that it be able to turn with a radius of 3.2 km at a constant speed of 800 km/h. The article states that tests show that the new wing structure will support a force 4 times the lift necessary for level flight. Is the wing structure sufficiently strong for the plane to make this turn?

13. Tension, Weight, Circular: A neighbor's child wants to go to a neighborhood carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks dangerous. She knows that you have taken physics and so asks your advice. The ride in question has a 10-lb chair which hangs freely from a 30-ft long chain attached to a pivot on the top of a tall tower. When a child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed. It rotates about the tower once every 3.0 seconds. When you ask the operator, he says that the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds and he weighs 200 lbs. Has the operator shown that this ride safe for a 50-lb child.

14. Pulleys, Friction: Block A (4.4 kg) rests on a table and is attached by a string and pulley to block B (2.2 kg) which hangs off the side of the table. Block C sits on top of block A. The coefficient of static friction between the two blocks is 0.20 and the coefficient of kinetic friction between block A and the table is 0.15. (a) Determine the minimum weight of block C such that it does not slide along block A. (b) Block C is suddenly lifted off block A. What is the acceleration of block A?

15. Friction: A cup of coffee sits on the dashboard of your car. You are driving along at 40 km/h and apply the brakes, bringing the car to a stop in 3.5 s. The cup of coffee is just about to slip along the dashboard as you stop. Determine the coefficient of static friction between the cup and the dashboard.

16. Composite Objects: A 2.0 kg block and a 1.0 kg block are connected by a string and are pushed across a horizontal surface by a 20 N force applied to the 1.0 kg block. The coefficient of kinetic friction between the blocks and the surface is 0.20. What is the tension in the string?

17. Tension: You are working out in a gym and are lifting a 10 kg mass using a rope with two handles. You notice while lifting the mass, the rope handles make a 15o angle with the horizontal. You estimate that the mass is accelerating upwards at 1.0 m/s2. What are the magnitudes of the two tension forces in the handle ropes? How hard should you pull if you want the ropes to be perfectly horizontal?

18. Friction, Normal: A student, whom we will call Bill, was about to go out on a date when his roommate, Bob, asked him to hold a pail against the ceiling with a broom for a moment. After Bill complied, the roommate mentioned the pail was full of water and left. Bill wants to slide the pail of water a few feet to one side so he can get to a chair in the room. The pail weighs 0.50 kg and has 3.0 kg of water in it. The coefficient of static friction between the broom and pail is 0.3 and the coefficient of static friction between the pail and ceiling is 0.5. Can Bill slide the pail?