Mechanics Problems - Force and Linear Kinematics Problems

Note: Each problem begins with a list of forces necessary to solve the context-rich problem. These are for the benefit of the instructor. Delete the list before using the problems in your class.

1. Weight, Normal: While driving in the mountains, you notice that when the freeway goes steeply down hill, there are emergency exits every few miles. 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 are curious, so you stop at the next emergency road. You estimate that the road rises at an angle of 10o from the horizontal and is about 100 yards (300 ft) long. What is the maximum speed of a truck that you are sure will be stopped by this road, even if the frictional force of the road surface is negligible?
   
   
2. Weight, Normal: While driving in the mountains, you notice that when the freeway goes steeply down hill, there are emergency exits every few miles. 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 50 ton truck going 70 mph up a ramp 100 yards (300 ft) long, even if the frictional force of the road surface is negligible.
   
   
3. Weight, Normal: You have opened a small delivery business that guarantees to deliver any box between 5 lbs. and 500 lbs. to any location in the area by the next day. At your distribution center, boxes slide down a ramp between the delivery and the sorting area. You must determine the angle this ramp should have so that a box will take 5.0 seconds to slide down the ramp when starting from rest at the top. When the box arrives at the bottom of the ramp, you decide that its speed should be no larger than 10 ft/s so as not to damage the contents of the box. Using the latest technology, the surface of the ramp will be extremely slippery.
   
   
4. Weight, Normal: You are watching a ski jump contest on television when you wonder how high the skier is when she leaves the starting gate. In the ski jump, the skier glides down a long ramp. At the end of the ramp, the skier glides along a short horizontal section which ends abruptly so that the skier goes into the air. You measured that the skier was in the air for 2.3 seconds and landed 87 meters, in the horizontal direction, from the point she went into the air. Make the best estimate of the height of the starting gate at the top of the ramp from the horizontal section from which the skier takes off into the air. Make clear on what assumptions your answer depends (this is why it is an estimate).
   
   
5. 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.
   
   
6. Weight, Normal, Friction: You have a summer job at a company that specializes in the design of sports facilities. The company has been given the contract to design a new hockey rink to try to keep the North Stars in town. The rink floor is very flat and horizontal and covered with a thick coat of ice. Your task is to determine the refrigeration requirements which gives best temperature for the ice. You have a table which gives the coefficient of static and kinetic friction between ice and the standard NHL hockey puck as a function of ice temperature. You have been told that the hockey game will be more exciting if passes are swift and sure. Experts say that the passing game is best if, after it goes 5.0 m, a puck has a speed which is 90% of the speed with which it left the hockey stick. A puck typically has a speed of 20 km/hr when it leaves the hockey stick for a pass.
   
   
7. Weight, Normal, Friction: You and some friends visit the Minnesota State Fair and decide to play a game on the Midway. To play the game you must slide a metal hockey-type puck up a wooden ramp so that it drops through a hole at the top of the ramp. Your prize, if you win, is a large, pink, and rather gaudy, stuffed poodle. You realize the secret to winning is giving the puck just enough velocity at the bottom of the ramp to make it to the hole. You estimate the distance from the bottom of the ramp to the hole at about 10 feet, and the ramp appears to be inclined with an angle of 10o from the horizontal. You just got out of physics class and recall the coefficient of static friction between steel and wood is 0.1 and the coefficient of kinetic friction between steel and wood is 0.08. The mass of the puck is about 2.5 lbs. You decide to impress your friends by sliding the puck at the precise speed on the first try so as to land it in the hole. You slide the puck at 8.0 ft/sec. Do you win the stuffed poodle?
   
   
8. Weight, Normal, Tension, Friction: Finally you are leaving Minneapolis to get a few days of Spring 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 45 miles/hour. 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.
   
   
9. Weight, Normal, Friction: While visiting a friend in San Francisco you decide to drive around the city. You turn a corner and are driving up a steep hill. Suddenly, a small boy runs out on the street chasing a ball. You slam on the brakes and skid to a stop leaving a 50 foot long skid mark on the street. The boy calmly walks away but a policeman watching from the sidewalk walks over and gives you a ticket for speeding. You are still shaking from the experience when he points out that the speed limit on this street is 25 mph. After you recover your wits, you examine the situation more closely. You determine that the street makes an angle of 20o with the horizontal and that the coefficient of static friction between your tires and the street is 0.80. You also find that the coefficient of kinetic friction between your tires and the street is 0.60. Your car's information book tells you that the mass of your car is 1570 kg. You weigh 130 lbs. Witnesses say that the boy had a weight of about 60 lbs and took 3.0 seconds to cross the 15 foot wide street. Will you fight the ticket in court?
   
   
10. Weight, Lift, Thrust, Drag: One morning while waiting for class to begin, you are reading a newspaper article about airplane safety. This article emphasizes the role of metal fatigue in recent accidents. Metal fatigue results from the flexing of airframe parts in response to the forces on the plane especially during take off and landings. As an example, the reporter uses a plane with a take off weight of 200,000 lbs and take off speed of 200 mph which climbs at an angle of 30o with a constant acceleration to reach its cruising altitude of 30,000 feet with a speed of 500 mph. The three jet engines provide a forward thrust of 240,000 lbs by pushing air backwards. The article then goes on to explain that a plane can fly because the air exerts an upward force on the wings perpendicular to their surface called "lift." You know that air resistance is also a very important force on a plane and is in the direction opposite to the velocity of the plane. The article tells you this force is called the "drag." Although the reporter writes that some metal fatigue is primarily caused by the lift and some by the drag, she never tells you their size for her example plane. Luckily the article contains enough information to calculate them, so you do.