Newton's Law-solutions

Newton's Law-solutions - le (txl65) Newtons Law mohanty...

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le (txl65) – Newton’s Law – mohanty – (81440) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A person oF mass 60 . 4 kg escapes From a burn- ing building by jumping From a window situ- ated 27 . 6 m above a catching net. The acceleration oF gravity is 9 . 8 m / s 2 . IF air resistance exerts a Force oF 79 N on him as he Falls, determine his speed just beFore he hits the net. Correct answer: 21 . 6509 m / s. Explanation: The Forces acting on him are the gravita- tional Force mg acting downward, and the air resistance, F a , acting upward. The accelera- tion is downward and the net Force is F net = ma = mg - F a a = mg - F a m The person is in Free Fall, so his fnal speed is defned by v f = 2 a h = r 2 ( mg - F a ) h m = R 2 [(60 . 4 kg)(9 . 8 m / s 2 ) - 79 N] (27 . 6 m) 60 . 4 kg = 21 . 6509 m / s . 002 10.0 points A spider oF mass m is sitting in a perFectly symmetric web (in a vertical plane with 45 angles between the web lines) as shown in the fgure below, where T i ’s denote the tensions along the lines which are connected to the spi- der at the center with i = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . The tension are all positive. T 1 T 2 T 3 T 4 T 5 T 6 T 7 T 8 m How is the tension T 3 related to T 2 , T 8 , and T 7 ? Hint: ±rom leFt-right symmetry, we see that T 1 = T 5 , T 2 = T 4 , and T 8 = T 6 . 1. T 3 = T 7 + ( T 8 + T 2 ) 2 + mg 2. T 3 = T 7 - ( T 8 - T 2 ) 2 - mg 3. T 3 = T 7 - ( T 8 + T 2 ) 2 - mg 4. T 3 = T 7 - ( T 8 - T 2 ) 2 + mg 5. T 3 = T 7 + ( T 8 - T 2 ) 2 + mg correct 6. T 3 = T 7 + mg 7. T 3 = T 7 + ( T 8 - T 2 ) 2 - mg 8. T 3 = T 7 9. T 3 = T 7 + ( T 8 + T 2 ) 2 - mg 10. T 3 = T 7 - ( T 8 + T 2 ) 2 + mg Explanation: Basic Concept Newton’s 2nd Law Solution: In the x (horizontal) direction, we have ( T 2 + T 8 ) 1 2 + T 1 - ( T 4 + T 6 ) 1 2 - T 5 = 0 , so, T 1 = T 5 , T 2 = T 4 , and T 8 = T 6 . In the y (vertical) direction, we have ( T 2 + T 4 ) 1 2 + T 3 - ( T 8 + T 6 ) 1 2 - T 7 - mg = 0 ,
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le (txl65) – Newton’s Law – mohanty – (81440) 2 and using the condition T 2 = T 4 and T 8 = T 6 , T 2 2 + T 3 - T 8 2 - T 7 - mg = 0 , or T 3 = T 7 + ( T 8 - T 2 ) 2 + mg . 003 10.0 points Beth, a construction worker, attempts to pull a stake out of the ground by pulling on a rope that is attached to the stake. The rope makes an angle of 68 . 9 with the horizontal. If Beth exerts a force of 133 N on the rope,
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This note was uploaded on 04/05/2011 for the course SD ds taught by Professor Sdsd during the Spring '11 term at Tarrant County.

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Newton's Law-solutions - le (txl65) Newtons Law mohanty...

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