Midterm with Solutions

Midterm with Solutions - Physics 230 MidTerm Examination...

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Unformatted text preview: Physics 230 MidTerm Examination Tuesday October 23rd, 2007 Each question is worth 10 points. Try all three, if you wish, but you will get points only for your best two. If you do not have time to finish a problem, but know how to do it, you can get points by showing the steps of your process without the complete solution. 1. (a) A pre-problem, providing a strong hint for the “real” solution. Two equal point masses, mass m , are hung on a string which passes over two pulleys at the corners of a block, as shown. One face of the block is at an angle θ to the vertical. The block rests on a flat surface, and is at rest. The mass which is hanging vertically just barely touches the block. There is no friction. Show that the acceleration of the two masses has magnitude a T = 1 2 g (1- cos θ ). Draw a diagram showing the forces on the two masses. Ideally, this should be on two separate diagrams! @ @ @ @ @ θ d d t t @ @ @ 6 ? t T mg t @ @ @ @I ¡ ¡ ¡ ¡ ? T N mg Both masses must have the same magnitude of acceleration, because the string connects them. Choose the acceleration of the left-hand mass to be positive down- wards. Equally, the tension that acts on the two masses has the same value. Thus mg- T = ma T and T- mg cos θ = ma T Solving, by eliminating T between these two equations:- T = mg + ma T = mg cos θ- ma T which gives the required result. 1 (b) A problem in an accelerated frame. Two equal point masses, mass m , are hung on a string which passes over two pulleys at the corners of a square block, as shown. The block rests on a flat surface. There is no friction. d d t t- a Then, the block is set in motion, with acceleration a to the right. Describe what happens by answering the following questions. Note: you are not expected to describe any oscillatory motion. Assume that any oscillations have decayed away. (c) One of the two masses will hang at an angle to the vertical face of the block. Which one? Illustrate your answer by drawing a free-body diagram for it in the accelerating frame. In the accelerating frame, there is a fictitious force in the opposite direction to a . This will push the right-hand mass towards the vertical surface, but it will push the left-hand mass away from the vertical. For the left-hand mass, therefore: t ¡ ¡ ¡ ¡ ? φ ma T mg (d) Draw a free-body diagram for the other mass, also in the accelerating frame. Now we must include the Normal force of the block: t- 6 ? ma N T mg 2 (e) What happens?...
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Midterm with Solutions - Physics 230 MidTerm Examination...

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