2008-2009 - Physics Final Exam Free Response Review Questions 1. Police detectives, examining the scene of a reckless driving incident, measure the skid marks of a car, which came to a stop just before colliding into a Wal-Mart to be 50.0 meters. It is known that the coefficient of kinetic friction µ k = 0.890 between the specific brand of rubber tires on the car and the road. The speed limit in the area is 20.0 m/s (about 45 mph). A. Assume the skid marks are straight and use Newton s laws and 1-D kinematics to determine if the driver of the skidding car was speeding before she began skidding? B. Sketch and clearly label the axes of three qualitative graphs of the car s acceleration, velocity and displacement as functions of time for the skid. 1
2. A medical relief airplane climbs to an altitude of 200. m and flies at a constant horizontal cruising speed of 80.0 m/s. The copilot steps to the back of the plane and opens the cargo door. She wants to drop a medical supply package to a landing site at a remote village A. Assuming the package is in freefall, use 2-D kinematics to predict how far (horizontally) before the plane flies over the village should the co-pilot drop the package such that it hits the landing site. B. Predict the final velocity of the package just before it strikes the ground. C. Sketch and clearly label the axes of three qualitative graphs of the package s acceleration, velocity and displacement as functions of time for the freefall. 2
3. Consider a free falling projectile with an initial velocity of 34.0 m/s @ 25.0 o above the horizontal. The projectile is shot from ground level on a planet different than Earth where the acceleration of gravity isn t known. The Range of this projectile is 180. m and it comes to rest at the same level at which it was shot: y o = y f = 0 meters. Use concepts from kinematics to predict the following: A. Predict the acceleration of gravity on this different planet. B. Predict the hang-time of the projectile (how much time will the projectile be in freefall.). C. Predict the velocity of the projectile at it s apex. D. Predict the height of the projectile s apex. E. Predict the final velocity of the projectile just before it strikes the surface of the planet. F. Sketch and clearly label the axes of three qualitative graphs of the projectile s acceleration, velocity and displacement as functions of time for the freefall. 3
Solution to problem 3 continued 4
4. Consider a 65.0 kg clown with an initial velocity of 10.0 m/s sliding up a rough circus slide inclined 38.0 above the horizontal and measuring 16.5 m along the diagonal. The coefficient of friction between the slide and the clown is µ k = 0.250. A. Predict the magnitude of the clown s acceleration along the slide. B. Predict the height of the highest point the clown will slide to. C. Predict the kinetic energy of the clown at it s highest point. D. Sketch and clearly label the axes of three qualitative graphs of the clown s acceleration, velocity and displacement as functions of time for slide up to the highest point. v o θ µ k h 5
Solution to problem 4 continued 6
5. A kinetic artist wants to build a life size double mass system in equilibrium, on an incline linear plane. The initial design consists of m 1 = 35.0 kg connected to m 2 = 17.5 kg by a thin, cable wrapped over a pulley. The artist hires you to predict the exact inclination angle at which the system will maintain static equilibrium without any help from friction. A. Predict the angle that maintains static equilibrium and get paid $750. B. If the inclined linear plane is rotated to ½ the angle equilibrium angle, which way will m2 accelerate neglecting friction? If the inclination angle is reduced, the system will accelerate such that the hanging mass will move downward. 7
6. Synchronous communications satellites are placed in a circular orbit that is 3.59 x 10 7 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance? 8
7. Consider a model airplane (1.90 kg) tied to a string and propelled by a small electric motor in a perfect horizontal circle with a circumference of 23.0 m at constant speed. The plane isn t really flying, instead a component of the string s tension is lifting the plane up against it s weight. If the sting makes an angle of 75 with respect to the vertical, then: A. Predict the length of the string. B. Predict the tension in the string. C. Predict the time it takes for the plane to complete one complete revolution. D. Sketch and clearly label the axes of a qualitative graph of the Tension in the string as a function of speed. T = 1.99 s Period of Revolution. 9
8. Consider a woman standing on a weight scale in a vertical elevator. Her mass equals 60.0 kg, and the combined mass of the elevator, scale and woman is 815 kg. Starting from rest, the elevator accelerates upward as a result of the hoisting cable applying a tension force of 1.05 x 10 4 N. A. Predict the apparent weight of the woman during the upward acceleration. B. Predict the apparent weight of the woman if the cable were to break and the elevator were in freefall towards the ground. C. Sketch and clearly label the axes of a qualitative graph of the women s apparent weight as a function of the elevator s acceleration. Briefly describe the physical meaning of the graph s two intercepts. 10
9. Consider a stunt jumper trying to leap her motorcycle across a narrow, but deep canyon. The stunt jumper drives her motorcycle horizontally off a cliff on one side of the canyon at a speed of 40.0 m/s and at a height of 75.0 m above the canyon floor and freefalls towards the ground. A. Predict the kinetic energy of the stunt jumper just before she lands on the ground. B. Predict the change in the stunt jumper s kinetic energy during the freefall leap. C. Predict the net work done during the leap. D. Predict the student jumper s final velocity just before hitting the ground. 11
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10. Consider a circus performer, starting from rest and sliding down a frictionless linear incline, continuing across a rough horizontal floor until they stop. Use the work energy theorem to solve this problem. A. Predict the kinetic energy of the circus performer at the bottom of the linear incline. B. Predict the speed of the circus performer at the bottom of the linear incline. C. Predict the length of the horizontal slide ( X) from the bottom of the linear incline the point where the clown comes to rest. h o = 25.0 m µ k = 0 37.0 = θ µ k = 0.300 X =? 13