Physics1201Q Final Exam Questions

Physics1201Q Final Exam Questions 1. A man stands on a platform that is equipped with rollers. The man holds a rifle aimed horizontally, with the rifle butt braced against the man’s shoulder. The man and the platform are both motionless. As part of a ballistics test, the man then fires the rifle so that the bullet travels horizontally in one direction and the man and platform move in the opposite direction to the bullet. Immediately after the bullet leaves the gun, the man and rolling platform have kinetic energy KE1 and the bullet has kinetic energy KE2. The bullet has mass m and the man plus platform have mass M. Find the ratio R, as given by R = (KE2 / KE1) in terms of M and m. 2. A box is placed on the outer rim of a horizontal disk that has an axle through its center. The disk is set to be spinning at constant angular speed with a period of 24 seconds. The radius of the disk is 4.6 m. How large must the coefficient of static friction be between the box and the disk for the box to stay on the rotating disk without slipping? 3. An oil drilling machine rests on the ocean floor about 5000 ft below the ocean surface. It drills through an additional 13,000 feet of soil when there is a failure and oil escapes through some kind of rupture. Assume the drill hole has a circular base consisting of the drill extending through a tall column of muddy paste, and that the diameter of this circular base is 18 cm.(a) Compute the approximate hydrostatic pressure at the base of the drill hole just before the failure. Assume the density of water is 1000 kg/m 3 and the density of the soil is 2.5 times that of water. (b) What would be the force on the circular base of the drill hole at this pressure? 4. Lake Champlain has a surface area of 1,126 km 2 . It freezes in the winter with an average ice thickness of 0.5 m. (a) What total energy does it take to melt the ice once spring comes? (b) If this energy is provided by sunlight shining on the lake at 200 W/m 2 , and this energy is only half absorbed, how long will it take the ice on the lake to melt? 5. A geosynchronous satellite stays above the same point on the equator as the earth revolves. Given the mass of the earth M, and gravitational constant G, find the distance D of the satellite from the earth’s center. 6. An oil spill on the ocean is sometimes modeled as having a velocity that has two components: a wind induced velocity that is 3% of the true wind velocity and an independent tidal velocity Vtidal. The tidal velocity is 3.0 km/hr due north and V wind = 40 km/hr 20 degrees north of east. In six hours, how far is the oil predicted to move in the northerly direction? 7. The above diagram illustrates the simple mass on a spring accelerometer. Note that were the acceleration to the right, instead of the left, the spring would compress rather than stretch. Let there be a vehicle with a flat top on which such an accelerator is fastened. The vehicle moves horizontally at all times and the accelerometer is also mounted horizontally as shown above. The mass on the spring is m, the spring constant is K, and the mass of the vehicle is M, where M >> m. The length of the unstretched spring is D, and the vehicle is moving at constant velocity to the west. Gradually the brakes are applied, and then held at constant braking force. The length of the spring is now observed to be L = D – b where L, D, and b are all positive numbers. What is the braking force on the vehicle in terms of given quantities? 8. For the regenerative braking system of a train, a cylindrical spinning flywheel is used to store energy. One train has a flywheel of mass 3000 kg, a diameter of 0.5 m, and attains an angular velocity of 8,000 RPM. If ten gallons of gasoline store 140 kw h of energy, how many gallons of gasoline are equivalent to the fully spinning flywheel in terms of energy storage?