PH141 Practice Exam 1

Name:_____________________ Physics 141 Exam #1 February 22, 2022, 5:10 p.m. - 6:40 p.m. You will have 1 hour, 30 minutes to complete this exam. Please budget your time accordingly. You may use a calculator and a single-sided sheet of handwritten notes. The exam has 4 scenarios and you must answer all 4. Please record your answers on this test paper; you may also attach additional paper. Grading Multiple Choice Questions (3 points each) Each scenario has 2 multiple choice questions associated with it. Clearly mark your choice. The answer choices will be rounded; please choose the closest answer. We will not look at any work you write for these questions, only your answer. Short Answer Questions (6 points each) Each scenario has one short answer question. For these questions, we care about your work as much as we care about your answer. Please show all of your work in the space provided. You need to show all of your work to receive full credit. If you carry over a mistake from the Multiple Choice Questions, you will not be double-penalized for that mistake on the Short Answer Question. Name and Signature on This Page (1 point each) Write your name on top and sign the Colorado State University Honor Pledge on bottom of this page. If you need extra space to complete a solution, please use the back page or attach additional paper, and clearly note that we should look at this work. Constants, Conversions, and Data g = 9.8 m/s 2 G = 6.673 x 10 -11 N·m 2 /kg 2 m Earth = 5.972 x 10 24 kg r Earth = 6.371 x 10 6 m ࠵? air = 1.2 kg/m 3 (at sea level) ࠵? air = 1 kg/m 3 (in Fort Collins) Distance from Earth to Sun = 1.4793 x 10 11 m Metric Prefixes: G = 10 9 ; M = 10 6 ; k = 10 3 ; m = 10 -3 ; μ = 10 -6 ; n = 10 -9 ; p = 10 -12 1 cm = 10 -2 m Honor Pledge I will not give, receive, or use any unauthorized assistance. Signature:______________________ This exam © 2022, Adam Pearlstein. All rights reserved.

Scenario #1: It’s Rocket Science A small rocket used to study the lower atmosphere has an engine which applies a time-varying thrust for an interval of 1.5 s. A simplified graph of the rocket’s acceleration versus time is shown on the right. The combined mass of the rocket and engine is 1.25 kg . Assume that the rocket starts from rest and that its motion is in a straight line for the entire 1.5 s that the engine fires. Neglect drag for this entire scenario. Multiple Choice Questions (3 points each): 1) What is the maximum net force on the rocket during the 1.5 s time interval when the engine fires? a) 0 N b) 20 N c) 40 N d) 60 N e) 80 N f) 100 N 2) What is the velocity of the rocket at the end of the 1.5 s time interval that the engine fires? a) 0 m/s b) 60 m/s c) 70 m/s d) 95 m/s e) 110 m/s f) 120 m/s Short Answer Question (6 points): Assume the rocket is launched from the ground with a launch speed given by your answer to Question 2 and a launch angle of 20º to the right of vertical. Express the initial velocity in component form using our standard choice of axes. What is the maximum height the rocket attains? How much time does it spend in the air before crash landing back on the ground? Assume the rocket is launched and lands at the same height. Note: You do not need to take into account the motion while the engine is firing for this Question. This exam © 2022, Adam Pearlstein. All rights reserved. Score for this scenario /12 acceleration (m/s/s) 0 20 40 60 80 100 time (s) 0 0.25 0.5 0.75 1 1.25 1.5

Scenario #3: I Gotta Run The speed of a particular sprinter as they go from rest to a top speed of 8.8 m/s can be modeled by where v is measured in m/s and t goes from 0 to 2 s. Multiple Choice Questions (3 points each): 5) What is the sprinter’s acceleration at t=0 s ? a) b) c) d) e) f) 6) How far does the sprinter run in 2 s ? a) 0 b) c) d) e) f) Short Answer Question (6 points): One way that runners can build strength during their training is to drag a weighted sled. Suppose a runner is wearing a harness connected by a rope to a 35 kg sled. The sled is on flat ground and at its connection to the sled, the rope makes an angle of 30º above the horizontal. The coefficient of static friction between the sled and the ground is given by and the runner pulls the rope with a tension of 350 N. What is the normal force of the sled on the ground? Is this tension in the rope sufficient to overcome friction and move the sled? v ( t ) = 8 t − 3 t 2 + 0.6 t 3 0 0.6 m / s 2 3 m / s 2 5 m / s 2 6 m / s 2 8 m / s 2 3.2 m 8.0 m 9.3 m 10.4 m 16 m μ s = 0.6 This exam © 2022, Adam Pearlstein. All rights reserved. Score for this scenario /12

Scenario #4: The Ski Jump Ski jumping is a sport where participants try to jump as far as possible after skiing down a large hill. S ki jumpers can extend their time in the air is by using drag force. To do this, they flatten their bodies and splay out their skis to increase their effective surface area. For this scenario, consider a skier falling at terminal velocity. Assume the skier has a height of 178 cm , mass of 65 kg , drag coefficient of 0.9, cross-sectional area of 1.1 m 2 , and that the density of air is 1 kg/m 3 . Multiple Choice Questions (3 points each): 7) What is the terminal speed of this ski jumper? a) b) c) d) e) f) 8) What is the magnitude of the drag force on this skier while they are moving at terminal velocity? a) b) c) d) e) f) Short Answer Question (6 points): The in-run to the ski jump is the large hill that skiers slide down to the gain speed needed for their jumps. Model an in-run as a 110 m -long flat ramp angled 37º below horizontal. The skier described above begins from rest at the top of the in-run and slides down to the bottom. Assume the coefficient of kinetic friction between the skis and the snow is . What is the skiers speed at the bottom of the in-run? 9.9 m / s 19.7 m / s 29.6 m / s 35.9 m / s 49.3 m / s 1290 m / s 0 N 337 N 437 N 537 N 637 N 737 N μ k = 0.2 This exam © 2022, Adam Pearlstein. All rights reserved. Score for this scenario /12 Total score for the exam /50