Download Constant Speed - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! PHYS1121 Physics 1a UNSW Test 1 2008 With answers Question 1 ( marks) You are cycling, on a long straight path, at a constant speed of 6.0 m.s–1. Another cyclist passes you, travelling on the same path in the same direction as you, at a constant speed of vb = 9.0 m.s–1. At the instant when she passes you, you realise that she is a friend of yours and you accelerate to catch up to her. You accelerate, starting from t = 0, the time when she passes you, with constant acceleration a = 1.5 m.s–2. a) i) On a displacement-time graph, sketch your position , xa(t), and the position of your friend, xb(t) as functions of time, for time t < 0 (i.e. while she is still behind you). Label these sections of the graphs xa and xb. ii) Also sketch displacement-time graphs for you your friend for time t > 0 (i.e. while she is still behind you). Label these sections of the graphs xa and xb. iii) Showing your working, derive both algebraic expressions and quantitative values for the time and distance it takes you to catch up with your friend. b) In part a, you accelerated with constant acceleration and overtook her. In this part, you accelerate with forwards acceleration a = 1.5 m.s–2 for a time T1, then decelerate with forwards acceleration a = −1.5 m.s–2 for a time Tb. You judge T1 and T2 so that when you stop decelerating, you are travelling alongside her at the same speed. Draw a second displacement-time graph to show this situation. Clearly mark xa, xb and the time intervals T1 and T2. Question 2 ( marks) i) Write Newton's second law in a form that applies to a finite object that is not necessarily rigid, but that has constant mass. If you statement is an equation, state carefully the meaning of each term. (For example, do not let the marker wonder "what force?" or "what acceleration?".) The sketches show successive states of a man jumping vertically in the air. He begins (sketch A) from a stationary position with his legs bent. He then straightens his legs and ankles rapidly: sketch B shows the moment at which his feet leave the ground. The lines marked "CoM" show the height of his centre of mass. Between the first two sketches, his centre of mass rises a distance L. Sketch C shows him at the point where his centre of mass has its maximum height, which is a vertical distance h above its height at the point of take-off. You may neglect air resistance. CoM CoM CoM L hA B ii) Showing your working, and stating any assumptions you make, determine the speed of the man's centre of mass at the moment (B) when his feet leave the ground. iii) Assume that the vertical acceleration acm of his centre of mass is constant between A and B. Derive an expression for acm. iv) Using your answer to part (i), and thinking carefully, derive an expression for the vertical force N exerted by the ground on his feet during the phase A to B. v) If the man's mass is 70 kg, if L is 0.4 m h is 0.6 m, what is the downwards force (assumed constant) exerted by his feet during the phase A to B? State any physical law or principle you use in obtaining your answer.
