Practice Exam 1

PHY 1 5 1 0 Midterm Exam 1 • Q. Ryan 2 Part I. Multiple Choice [32 points total] Circle the correct answer to each question. 8 questions, 4 points each 1. What are the overall dimensions of the formula for the area of a circle ! ! ! ? A. [ ! ] B. [ ! ] ! C. ! ! D. ! [ ! ] ! E. ! ! ! 2. The graph below shows the velocity vs. time for a train moving along a straight track. The graph shows that during the time shown the train… I. Always moves in the same direction II. Reverses direction during its motion III. Has both a positive and a negative acceleration A) Only one of the statements is correct B) Statements I and II are correct C) Statements I and III are correct D) Statements II and III are correct E) All three statements are correct 3. A projectile is launched from the origin of a coordinate system with initial velocity v 0 at angle θ 0 from the horizontal (0 < θ 0 < 90°). At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity, and acceleration vectors are r , v, and a ( bold symbols denote vectors ). Which statement is true? Hint: draw a diagram. A. r is parallel to v . B. r is perpendicular to v . C. v is parallel to a . D. v is perpendicular to a . E. r is perpendicular to a .

PHY 1 5 1 0 Midterm Exam 1 • Q. Ryan 3 4. The velocity of a particle moving along the x -axis is given by ! ( ! ) = ! ! + !" , where t is time in seconds. We define our coordinate system such that for t = 0, the initial position is x 0 = 0 and the initial velocity is v 0 . Which expression describes the position of the particle as a function of time? A. ! ! = ! ! ! + ! ! ! ! ! B. ! ! = ! ! ! + ! ! ! ! C. ! ! = ! ! ! + ! ! ! ! D. ! ! = ! ! ! + ! ! ! ! E. none of the above 5. What is the direction of the vector given by A − B + C ? A. ↑ Up B. ↓ Down C. ← Left D. → Right E. ↖ Up and Left 6. A car drives clockwise around a circular racetrack at a steady speed. At the instant when the car is located at the position indicated by the dot: A. the car’s acceleration points north B. the car’s acceleration points south C. the car’s acceleration points east D. the car’s acceleration points west E. none of the above N S E W

PHY 1 5 1 0 Midterm Exam 1 • Q. Ryan 5 Part II. Problems [68 points total, partial credit possible] Show ALL of your work for each part of the following questions to get full credit. 1. [20 points total] A block (A) and a cart (B) and are connected by a light string which passes over a massless and well-oiled pulley. The mass of the block (A) is 5kg and the mass of the cart (B) is 10kg. The kinetic frictional coefficient between the cart and the track is 0.2. Block A is moving downward and Cart B is moving to the left as shown in the picture. If you cannot solve a given part of this problem, you may solve the remaining parts algebraically and assume you know the variable you need from a previous part. A. [3 points] Draw the free-body diagram on the block (A) and the cart (B) respectively. ( Hint: Label all the forces you draw.) B. [5 points] What is the magnitude of the acceleration of the block (A)? A B

PHY 1 5 1 0 Midterm Exam 1 • Q. Ryan 6 C. [8 points] What is the magnitude of the tension force of the string? D. [4 points] What is the static frictional coefficient required between cart B and the track so that the cart and the block can be at rest? Hint: The maximum static friction between an object and the surface is: ! F f = μ s ! N μ s is the static frictional coefficient, ! N is the normal force

PHY 1 5 1 0 Midterm Exam 1 • Q. Ryan 8 c. [15 points] Solve the problem.

PHY 1 5 1 0 Midterm Exam 1 • Q. Ryan 9 3. [18 points total] A cargo plane is flying at a speed of 200 m/s at an altitude of 500 m when it drops a package of relief supplies. Unfortunately, the parachute on the package does not open and the package falls as an object in free fall with negligible air resistance. a) [3pts] Draw the path of the package after it leaves the plane. b) [5pts] Show, using appropriate velocity vectors, the direction of the average acceleration between the point when the package leaves the plane and the point just before the package hits the ground. c) [10pts] Calculate the speed of the package just before it hits the ground.