PracticeFinal - These are practice problems for the Fall...

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These are practice problems for the Fall 2007 8A final. There is no guarantee as to whether they will or won’t be on the final. These are not representative of all the questions on the final; one or more final exam questions are likely to come from homework, discussion/lab section, and/or lecture. No solutions will be provided; the value in these problems come from struggling with them until you understand them for your self. If you’d like to know whether you’ve understood them, send a rough summary of how you did the problem to me and I’ll let you know – Bob 1) Energy A 50-kg skier climbs slowly up a hill of height 30m. Starting from rest, he then skies from the top of the hill to a point 10 m above the bottom of the hill, where his speed is 5 m/s. a) How much work does the skier do in climbing the hill against gravity? How much work does gravity do on the skier during the climb? b) One kilogram of fat supplies about 4 x 10 7 Joules of energy. The body converts fat into mechanical energy with 20% efficiency. How many kilograms of fat does the skier use in climbing the hill? c) What happens to the other 80% of the energy stored in fat? d) How much work is done on the skier by the friction between the snow and his skies and air resistance? 2) Oscillations A mass M = 1 kg is attached to two springs with spring constants k 1 = 5 N/m and k 2 = 20 N/m as shown. At t = 0 the mass is released from rest at a distance x o = 1 m from its equilibrium point. a) What is the period of oscillation? b) Write down the position of the mass as a function of time. c) What is the total mechanical energy of the system?
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