Displacement Time Graph - Physics - Exam Paper, Exams of Physics

Download Displacement Time Graph - Physics - Exam Paper and more Exams Physics in PDF only on Docsity! 5 Question 1. [Marks 20] (a) An unmarked police car P is, travelling at the legal speed limit, vP, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding – ie travelling at constant speed vC > vP. At t = 0, the police car begins to accelerate at constant acceleration, a, for time T1. It then decelerates, at constant acceleration, –a, for a time T2. The police car driver judges T1 and T2 so that, at time t = T1 + T2, the police car is alongside the speeding car and travelling at the same speed, vC. Draw a displacement-time graph to show this sequence. Clearly mark the displacements xP and xC of the two cars and the time intervals T1 and T2. Please make the drawing clear (and draw a second one if the first one is too messy). Make sure you indicate on the graph the relative size of the time intervals, T1 and T2. (b) State Newton's second law of motion for a particle, defining carefully each term used. (c) R Path of carriage Beam This is a sketch of a circus ride. A beam connects two carriages, in which people ride, secured by seatbelts. The beam rotates about a horizontal axis through its centre, so that the path of the carriages is a circle, radius R, in a vertical plane (as shown). The mass of the carriage (passengers included) is m. The mass of the beam is negligible compared to that of the carriages and the size of the carriages is negligible compared to the length of the beam. The beam rotates at constant angular velocity with period T. Consider the moment when the beam is vertical, as shown. (i) Derive one expression for the tension Ftop in the top half of the beam and another expression for the tension Fbottom in the bottom half of the beam, in terms of T and other quantities. (ii) Derive an expression for the value of T for which the tension in the beam is zero in the top half of the beam, when vertical. (iii) Describe the behaviour of unsecured objects in the upper carriage during condition described in part (ii). How would they appear to someone inside the carriage? 6 Question 2. [Marks 14] A spacecraft (with mass m) is in circular orbit (with radius r) around the earth (mass M), above the equator. With respect to a point below it on earth, it is travelling towards the East at speed v. (i) Write an expression for the mechanical energy of the spacecraft in terms of M, m, v, r and G. Specify the reference state for potential energy. (ii) Using Newton's second law, relate v and r to the gravitational force between the earth and the satellite. (iii) Hence or otherwise derive an expression for kinetic energy K as a function of M, m, r and G. (iv) Using the previous results or otherwise, derive an expression for the mechanical energy of the orbit as a function of M, m, r and G. (v) Write an expression for v as a function of M, m, r and G. 9 Question 5. [11 Marks] (a) A 7.00 kg object is hung from the bottom end of a vertical spring fastened to an overhead beam. When the object is set into a vertical oscillation, it is found to have a period of 2.60 s. Find the force constant of the spring. (b) Refer to the figure below. A piezo-electric buzzer, emitting a frequency of 3.00 kHz, is mounted on a vertical cantilever spring so that it oscillates horizontally at 10 Hz with simple harmonic motion. The amplitude of this simple harmonic motion is 40 cm. A microphone is mounted on the horizontal line of the buzzer’s motion. microphone spring buzzer Determine the highest and lowest frequencies received by microphone. Assume that the speed of sound is 343 m/s, and ignore reflections from the floor. 10 Question 6 [Marks 13] (a) As shown in the Figure below, an object is hung from a string (with linear mass density µ = 0.00200 kg/m) that passes over a light pulley. The string is connected to a vibrator (of constant frequency f), and the length of the string between point P and the pulley is L = 2.00 m. When the mass m of the object is either 16.0 kg or 25.0 kg, standing waves are observed; however, no standing waves are observed with any mass between these values. Note: The amplitude of the vibrator is much smaller than that of the standing waves produced, so you may treat the vibrator as a displacement node. (i) What is the frequency of the vibrator? (Note: The greater the tension in the string, the smaller the number of nodes in the standing wave.) (ii) What is the largest object mass for which standing waves could be observed? (b) A piccolo is a musical instrument with an overall length of 32.0 cm. The resonating air column can be approximated as a cylindrical pipe, ideally open at both ends. Find the frequency of the lowest note that a piccolo can play, assuming that the speed of sound in air is 343 m/s. L L Frequency Generator m P µ