Quiz Number 1 PHYSICS January 30, 2009

Transcription

1 Instructions Write your name, student ID and name of your TA instructor clearly on all sheets and fill your name and student ID on the bubble sheet. Solve all multiple choice questions. No penalty is given for wrong answers. Solve each problem on a different sheet of paper. Turn in the bubble sheet and solution sheets only. Do not return the cover sheet and the multiple choice sheet. Solutions to the problems should begin from the following basic physical principles: If x(t) is the position of the object as a function of time than velocity is v(t) = dx dt and acceleration is a(t) = d2 x dt 2. When the acceleration is a constant a then x(t) = x 0 + v 0 t at2. Show all steps in the derivation of the answers. Make sure you write neatly and orderly. It is YOUR RESPONSIBILITY to make sure that the grader understands your solution. S/he will not give full points if they can not follow the solution, even if the final answer is correct. The acceleration due to gravity on Earth is 9.8 m/s 2. The solutions to the quadratic equation 0 = ax 2 + bx + c are given by x = b± b 2 4ac 2a. The following derivatives and integrals may be useful: If y(x) = Ax m, where A and m are constants, then Z y dx = dy dx = Amxm 1 A m + 1 xm+1, for m 1 You can use a calculator. Page 1

2 Last name : First name : Student id : TA : Problem 1 (25 points) You have an internship at the State Capitol with the state public safety commission. Your task is to help develop new specifications for the police crusiers used by the State Patrol. In particular, you are working on the acceleration requirements. Patrol officers would like to have the largest acceleration possible, but more acceleration means a bigger, more expensive engine and more fuel usage. After some discussion, the patrol officers agree that they should be able to catch up with a vehicle travelling at 180 kilometers per hour within two kilometers of constant acceleration. How much acceleration (in m/s 2 ) would be needed? a) Both the speeder and the patrol car start at x = 0. The speeder has a constant velocity of 180 kph = 50 m/s. The patrol car has an initial velocity of zero. The two cars must travel two kilometers in the same amount of time. b) x s = v s t, with v s = 50.0 m/s and t in units of seconds. c) x p = 1 2 at2, with t in units of seconds. d) The two must meet when x s = x p = 2 km, so v s t = 2 km. t = 2 km v s = 40 s. e) Given the time and distance, we can now determine the necessary acceleration. x p = 1 2 at2 a = 2x p t 2 = 2.5 m/s2 Page 2

3 Last name : First name : Student id : TA : Problem 2 (25 points) You are having a fun afternoon flying your remote control airplane when suddenly the airplane flys past you and stops responding to your controls. You watch it fly away in a level straight line across the open farm fields and you have no car to follow. As it gets smaller, you have a sudden thought on its current path, it will run right into a hill 2 kilometers away, so you call a friend of yours who lives 5 kilometers away from the point where the plane will stop. She is willing to go grab your plane as it goes by, but she is watching her favorite cooking show and doesn t want to leave any earlier than she has to, while you don t your plane to be lying on the side of the hill any longer than necessary. You know from experience that your plane will travel at 2 m/s for another eight minutes before the main battery dies and it slows down to 0.8 m/s. Your friend will average 20 m/s on her snowmobile. How long after the airplane passed you should your friend leave to be able to get it as soon as it lands? a) Make a diagram showing the paths of the airplane and your friend. Take origin of both paths to be the meeting point 5 km (x a = 0 = y f ). b) The first thing to determine is the time taken by the airplane to reach the road. The motion of the airplane has two parts: the first part is 8 minutes long and has a velocity of 2 m/s and the second part has a velocity of 0.8 m/s and an unknown time. The total displacement of the two stages is 2 km. 2 km 8 min 2 km = 2 m/s 480 s m/s t 2 t 2 = 2 km 2 m/s 480 s = 1300 s 0.8 m/s So the total time for the airplane to reach the road is 1780 s. c) Once your friend jumps on her snowmobile, it will take her t = 5 km 20 m/s = 250 s to get to where the plane will cross. d) Combining all the information, your friend should leave = 1530 seconds after the plane passed you to just catch it. Page 3

4 Multiple Choice Questions (5 points each) Question 1 : The speed of waves on a stretched string is known to depend only on the mass per unit length and the tension τ on the string. Tension has dimensions of [M][L] [T ] 2. Based on dimensional analysis, what combination of and τ is proportional to the wave speend v? A) v τ B) v τ C) v τ D) v τ E) v τ The correct answer is D. Question 2 : A BlueRay DVD with dimensions as shown in the figure can hold bits (25 GB). Estimate the area used for a single bit on the surface of the CD. 1.5cm 6 cm A) 500 µm 2 B) 0.05 µm 2 C) 5.0 nm 2 D) 20 m 2 E) 5.0 µm 2 The correct answer is B. Question 3 : Consider three vectors : Calculate A C 2 B. A) î 5 ĵ 1ˆk B) î 3 ĵ + 2ˆk C) 5î 5 ĵ 4ˆk D) î 5 ĵ + 2ˆk E) î 5 ĵ 2ˆk A = 2î 3 ĵ B = 2î ˆk C = î + 2 ĵ + 3ˆk The correct answer is A. Page 4 (NEXT PAGE)

5 Question 4 : Which of the graphs of position versus time below could represent a relay race with the second runner moving faster than the first? The correct answer is D. Question 5 : The velocity of an object as a function of time is given by v(t) = 9.00 m/s + (3.50 m/s)t (1.50 m/s 2 )t 2. Determine the instantaneous acceleration at time t = 5.00 s. A) m/s 2 B) 7.00 m/s 2 C) 2.50 m/s 2 D) 0.00 m/s 2 E) 4.00 m/s 2 The correct answer is A. Page 5