NATION TAIWAN UNIVERSITY PHYSICS DEPARTMENT General physic (202-10501 Class 10) Midterm Exam ,fall 2003 Tuesday November 18 2003, 10:20-12:20 Instruction : Closed books and notes Answer all question. You can only use one dictionary and one calculus without any prestored formulas. 1.A particle of mass M moves in the x-y plane wiht its x and y coordinate as following functions of time: x=e^-btcos(wt) y=sin(wt) where b and w are constants a) Describe the trajectory of the particle b) what is the velocity of the particle as a function of time? c) what are the x and y components of the force acting on this particle ? d) what is the condition under which the force acting on the particle is conservative ? Find the potential energy of the particle under this condition, and show that tje mechanical energy of the particle is conserved 2. a gun is located on the ground at the distance b from a flagpole of height H. the gun is aimed at a fixed angle of elevation θ (assume tanθ>H/b) a) what is the muzzle velocity of the shell in order to hit the top of the flagpole? b) if the flagpole were removed , at what distance form the gun would the shell strike the ground ? 3. an object is fixed at the surface of a planet which is identical in mass and radius of the earth . if the object experiences zero gravity at the equtor of that planet, what is the length of a day on that planet ? mass of earth 5.98*10^24kg radius of earth 6.37*10^6m Gravitational constant 6.67*10^-11 N*m/kg^2 4.an election of mass m collides head-on with an atom of mass M, initially at rest . As a result of the collision an amount of energy of E is stored internally inside the atom . What os the minimum initial velocity of the electron ? 5.A thin string is wrapped around a solid cylindrical spool of radius R and mass M . One end of the string is fixed , and the spool is allowed to fall vertically , start from rest , as the string unwinds. RECLL that the moment of inertia of solid cylinder is MR^2/2 a) Determine the angular momentum of the spool about its center of mass as a functin of time ? b) What is the tension is the string as a function of time ? 6. Consider an idealized chain piled up at a point next to a hole in a table. Let the chain have mass ρ per unit length . If one end of the chain is allowed to slip through the hole , it will start to fall and pull the rest of the chain through . How does the lower end of the chain move as a function of time ? What is the acceleration of the chain ? Is the total mechanical energy conserved in the process ? explain your answer --

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