RH= 1'55 CH1= I100 CH2= I10 PHYS 150 TEST #2 10/8/21 Dr. Holmes NAME Key DO ALL EIGHT PROBLEMS. SHOW YOUR WORK FOR PARTIAL CREDIT. ALL ANSWERS SHOULD BE IN MKS UNITS UNLESS OTHERWISE SPECIFIED! MASS OF EARTH = 6.0 x1024 kg; RADIUS OF EARTH = 6,380 km. 1) An object at the top of a building 13 meters above the ground is thrown up and out away from the building with an initial speed of 32 m/s and an initial angle of 67 above the horizontal. Neglecting air resistance, how high will the object go at its highest (as measured from the ground level at the base of the building? [5] 57.3 m . b) How long a time did it take for the object to reach its maximum height? [5] 3.01 sec . c) How far from the building did the object land on the ground? [3] 80.3 m VD = 32 m/s Do = 67 2) An SR-T1 jet reconnaissance plane is to make a high speed turn when going at a speed of 1,200 mfs. The circular acceleration should be 5 gees (49 mfsz) since any more may cause the pilot to black out. a) What is the radius of the turn if the velocity is 1,200 mls and the acceleration is 49 mlsz? = 18.3 miles [5] 29,388 m . b) How long (a time) will it take to make a complete circle under the above conditions (that is, what is the period)? = 2 min 34 sec [5] 154 sec . c) What is the angular velocity (in radi'sec) in this circular orbit? [5] 0.041 radlsec . PHYS 150 Test #2 page 2 3) A boat on a calm lake can go at a speed of 8 mi's. This same boat is used on an "ideal" river that ows at a uniform and constant rate of 3 mls Southward. a) If the boat is on the West bank, which direction should you head the boat if you want to cross the river to a point directly opposite (East of) your starting position? [Answer in angles from standard directions, such as 45 East of North or 22" South of West] [3] 22.0 N of E . b) If the river is 250 m wide, how long a time will the crossing take? [3] 33.7 sec . c) If you wish the boat to cross the river in the LEAST TIME, what direction would you head the boat? [3] due East . d) How long a time is this least time? [3] 31.25 sec . 4) A weight is held up by a rope attached to the ceiling and a rigid bar attached to a side wall and pivoted so it is free to rotate as shown below in the figure. The weight is 250 Mt, Ompc=80 (angle with ceiling) and Brod = 66 (angle with the wall). Neglect the weight of the rope and rod. a) Will the rod be pulling down and to the left or pushing up and to the right? [3] ug & right . b) Will the sum of the magnitudes of the tension in the rope and pull or push of the rod be [equal to, greater than, or less than] the weight? [3] greater than . c) What is the tension in the rope? [a] 235.4 Nt PHYS 150 Test #2 page 3 5) A car of mass of 1,850 kg can accelerate from 0 to 29 m/s in 7 seconds. a) What is the average acceleration of the car? [4] 4.14 m/s2 b) What is the net force (resultant) exerted on the car to make it accelerate at that rate? [4] 7,664 Nt c) What is the weight of the car? [4] 18,130 Nt 6) Consider an object on a scale in an elevator. At one particular instant the elevator has an acceleration of +1.8 m/s? and a speed of -2 m/s. (Plus means up and minus means down). a) Is the elevator speeding up (going faster whether positive or negative), slowing down (speed approaching zero), or maintaining its speed? [3] slowing down _. b) If the scale reads 700 Nts at this instant when the acceleration is +1.8 m/s and the speed is -2 m/s, is the weight of the object more than 700 Nts, equal to 700 Nts, or less than 700 Nts? [3] less c) If the motion of the elevator changes so that the scale now reads 650 Nts, is the new acceleration of the elevator more than +1.8 m/s2 (even bigger positive value), still = +1.8 m/s?, or less than +1.8 m/s? (smaller positive or even negative value)? [3] less _. d) When the elevator has an acceleration of +1.8 m/s and the scale reads 700 Nts, what is the mass of the object located on the scale? [5] 60.34 kgPHYS 150 Test #2 page 4 7) Consider a car that is making a right (>) turn on a road that is banked to help the car around the turn. Assume that the engine is proving just enough force to balance the air resistance so that the car maintains its initial speed during the turn. a) DRAW A DIAGRAM of this situation, and on the diagram INDICATE the direction of all the forces (except the force of the engine and the air resistance force) on the car. Be sure to show how the road is banked, and indicate the angle on the diagram. [4] b) On the diagram above, indicate the direction of the resultant acceleration of the car. [2] c) Set up the equations of motion (Newton's Second Law) for the car: [4] 8) A 50 kg satellite is to be put into orbit around the larger of Mars' two moons, Phobos, that has a radius of 11.1 km and a mass of 1.08 x 1015 kg. Assume Phobos has a spherical shape not quite accurate but good enough for our purposes. The satellite is to orbit at a height above Phobos of 8.9 km (5.5 miles) so the radius of orbit = 20 km. a) What is the force of gravity due to Phobos on the satellite while it orbits at this radius? [3] 0.090 M . b) What will the period of orbit of this satellite be? = 349 min = 5 hours 49 min [3] 20,939 sec . c) What speed should this satellite have in order to have a circular orbit at this radius with this period? [3] 6 ml's . d) What is the acceleration due to gravity (gPhobos) on the surface Phobos? [3] 5.35 x 10'3 ms2