Physics 111 n final exam

Physics 111 N Final Exam Please answer all problems on the blank paper provided. Clearly print your name and student ID on every sheet you use. Please hand in your formula sheet along with your answers Course ID : 10076 Prof. Jozef Dudek Unless instructed otherwise, you must show working, or explain how you came to your answer for all questions. You cannot get full credit on a question unless working is shown. Partial credit will be awarded for working which is partially correct. Drawing appropriate labeled diagrams may be of help. There are nine(9) questions plus two(2) bonus questions for extra credit. You have 3 hours to complete as much of the test as you can. 3 3 The density of water is approximately 1. 00 × 10 kg/m Take the universal gravitational constant to have the following value: G = 6. 67 × 10−11 Nm2 kg−2 Take the magnitude of acceleration due to gravity at the surface of the Earth to have the following value: g = 9. 80 ms−2 Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 1. [1. 1] Two cars travel on the parallel lanes of a two-lane road. The cars’ motions are represented by the position versus time graph shown in the ï¬�gure. 1. at what time do the cars pass one another? At this time are they traveling in the same direction? 2. at what time (if any) does car #1 momentarily stop? At what time (if any) does car #2 momentarily stop? 3. where is car #1 when car #2 changes direction? 4. what is the average velocity of car #1 in km/hr? 5. estimate the instantaneous velocity (in km/hr) of car #2 at t = 43 min ? x / km car #1 20 10 car #2 0 20 10 30 40 t / min [1. 2] Here is a plot of velocity versus time for an object that travels along a straight line (positive direction to the right) with a varying velocity. v/ m/s 1. at what time(s) is the object at rest? 20 2. what is the average acceleration for the ï¬�rst 20 secs? 3. during which periods of time is the object moving to the left? 10 4. what is the velocity at t = 30 s? 0 -10 Physics 111N 10 20 30 40 t /s [15 points] FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 2. [2. 1] A ball is tossed vertically into the air, when it reaches the highest point in its trajectory it has (a) velocity pointing upward and zero acceleration (b) zero velocity and zero acceleration (c) zero velocity and acceleration pointing downward (d) velocity pointing downward and acceleration pointing downward [2. 2] At one instant in time an object has the velocity and acceleration vectors shown, which of the following is true for the object a very short time later: a v (a) the object has slowed down (b) the object has sped up (c) the object is moving in a di! erent direction at the same speed (d) it is not possible for acceleration to be perpendicular to velocity [2. 3] The pilot of an Eksian bomber plane fl ying horizontally at 20 m/s releases a 10 kg bomb hoping for it to land on the Wiyan trench. Eksian 1. Sketch the trajectory of the bomb. bomber 2. How many seconds after release does 20 m/s the bomb hit the trench (100 m below the plane) ? 3. What is the horizontal distance from the bomber (when the bomb is released) to 100 m the Wiyan trench? 4. What is the speed of the bomb when it reaches the trench? What would the speed be if the bomb was of mass 20 kg? 5. The Eksian trench is 130 m horizontally from the position of the bomber when the bomb is released. At what speed would the bomber have to be traveling for the 10 kg bomb to hit the Eksian trench? Wiyan trench Eksian trench [20 points] Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 3. [3. 1] A greased block of mass 20 kg is pulled along a smooth horizontal surface by a string as shown below. The grease reduces friction with the surface to zero. 20 kg 1. Draw a labeled free-body diagram indicating all the forces on the block. 2. If the block is accelerating to the right at 4. 0 m/s2 , what is the magnitude of the tension in the string? 3. What is the magnitude of the normal force of the surface on the block? 4. What is the magnitude of the force applied to the surface by the block? Explain your answer [3. 2] The string is cut when the block is moving to the right at a speed of 10 m/s. 1. Draw a labeled free-body diagram after the string is cut. 2. 10 seconds after the string is cut what is the speed of the block? [3. 3] The grease is removed from the block so that there is now friction between the block and the surface with coe” cient of kinetic friction µk = 0. 5. The block is pulled by a reattached horizontal string so 2 that it accelerates at 3. 0 m/s 1. Draw a labeled free-body diagram from the block. 2. What is the tension in the string? 3. Describe briefl y what will happen to the block if we cut the string. [20 points] Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 4. [4. 1] Consider the two frictionless inclined planes shown. A block of mass m1 is placed at the top of plane 1 and a block of mass m2 is placed at the top of plane 2. The initial height is the same. Both masses are released, which has the larger speed at the bottom of m1 m2 the plane? (a) mass m1 (b) mass m2 (c) they have the same speed (d) it depends upon which mass is larger 45o 30o Explain your answer. [4. 2] Alan the skateboarder moves down a quarterpipe of radius 4. 0 m. The mass of the skater and his board is 30. 0 kg. If he starts from rest and there is no friction, what is Alan’s speed at the bottom of the ramp? [4. 3] Brendan is a heavier skateboarder – he rides the quarterpipe starting from rest, how does his ï¬�nal speed compare with Alan’s? Explain your answer. [4. 4] Actually there is some friction between the board and the ramp and Alan’s speed at the bottom of the ramp is measured to be 6. 00 m/s. How much work was done by the frictional force acting on him? Explain briefl y why the normal force of the ramp on Alan never does any work on him. [15 points] Question 5. [5. 1] A regulation 0. 145! kg baseball can be hit at speeds of 45 m/s. What momentum does the ball have? What kinetic energy does the ball have? [5. 2] If a line drive is hit essentially horizontally at this speed and is caught by a 100 kg player who has leapt directly upward into the air, what horizontal speed (in m/s) does he acquire by catching the ball? Solve this by conserving total horizontal momentum. [5. 3] By how much does the total kinetic energy of the system change (neglect any vertical motion)? Is this collision elastic? [10 points] Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 6. [6. 1] When a mass attached to a spring obeying Hooke’s law is released from rest 3. 0 cm from its equilibrium position it oscillates with frequency f . If the mass were released from 6. 0 cm it would oscillate with frequency √ 2f 2f (a) (b) (c) f (d) f /2 Explain your answer. [6. 2] A mass attached to a spring is oscillating in a horizontal plane. When it passes through its equilibrium position its energy is (a) purely kinetic (b) purely potential (c) partly kinetic and partly potential (d) zero ? Explain your answer. [6. 3] A bass guitar string of length 100 cm is ï¬�xed at each end and is oscillating in a standing wave as shown: 1. Is this mode (a) the fundamental ? (b) the ï¬�rst overtone ? (c) the second overtone ? 2. What is the wavelength of this standing wave? 3. The frequency of this wave is 41 Hz, what is the speed of wave-propagation on this string? 4. Another string (of the same length) on the same guitar has total mass 15. 0 g and waves on it are measured to travel at 120 m/s. What is the tension in this string? [10 points] Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 8. 24 [8. 1] The Earth has a mass of approximately 6 × 10 kg. The moon orbits orbits the center of the Earth at an average radius of about 4 × 108 m. We can approximate the moon’s orbital path by a circle. 1. If the only force on the moon is the gravitation attraction to the Earth, what is the moon’s acceleration? 2. What is the linear speed of the moon around its circular orbit? 3. What orbital period does this give (in days)? [12 points] Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek Question 9. [9. 1] As shown below, a woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows: P is the upward force being exerted on the crate by the woman, N is the contact force on the crate by the fl oor, and W is the weight of the crate. How are the magnitudes of these forces related, while the person is trying unsuccessfully to lift the crate? Explain your reasoning including a free-body diagram for the crate and a statement about the acceleration of the crate. (a) P + N < W (b) P + N > W (c) P = N (d) P + N = W [9. 2] A unstretched spring is 12. 00 cm long. When you hang a 875 g mass from it, it stretches to a length of 14. 40 cm. 1. What is the force constant (in N/m) for this spring? 2. What total mass must you hang from the spring to stretch it to a total length of 17. 72 cm? [8 points] Physics 111N FINAL EXAM Physics 111 N Final Exam Course ID : 10076 Prof. Jozef Dudek BONUS QUESTION #1 Block A weighs 90. 0 N. The weight w is 12. 0 N and the system remains at rest. 1. Find the frictional force on A. 2. Find the maximum weight w for which the system will not move if the coe” cient of static friction between the block and the table is 0. 33 . Illustrate your answers with appropriate free-body diagrams. [15 points] BONUS QUESTION #2 A light rope is wrapped several times around a large wheel of radius 0. 400 m. The wheel rotates on frictionless bearings about a stationary horizontal axis as shown in the ï¬�gure. The free end of the rope is tied to a suitcase of mass 15. 0 kg. The suitcase is released from rest at a height 4. 00 m above the ground. The suitcase has a speed of 3. 50 m/s when it reaches the ground. Calculate the moment of inertia of the wheel. In solving this problem, draw free-body diagrams for the suitcase and the wheel, compute the suitcase’s acceleration and the angular acceleration of the wheel (you may wish to use the relation between linear and angular acceleration a = Rα ). [20 points] Physics 111N FINAL EXAM