1. a light spring with spring constant 1200 n/m has a 55g object at its end. (a)
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Question
1. a light spring with spring constant 1200 n/m has a 55g object at its end. (a) If the energy of the system is 6.0J what is the amplitude of the vibration? (b) What is the maximum speed of the object? (C) What is the speed when the object is at a position x= A/2? What assumptions did you make?
2. Determine the frequency of vibration for an spring mass system that has a mass of 100 grams a spring constant of 20 N?m and the distance from the +A to -A is 0.40m . Determine the maximum speed of the System Assuming the period is the same for the pendulum determine the pendulum length
3. A logitudinal wave of amplitude 3.0 cm frequecny 2.0 Hz and speed 3.0 m/s travels on an infinityly long Slinky. How far apart aare the two nearest points on the slinky that at one partticualt time both have maximum displacements from their equilibrium positions? Explain your reasoning.
4. A wooden flute open at both ends is 0.48 m long (a) Determine its fundamental vibration frequency, (b) How far from one end should a finger hole be placed to produce a sound whose frequency is four thirds that calculated in part (a) . What Assumptions are there in this?
5. Light is an incident on the boundarybetween 2 media at an angle of 32 degrees. If the refracvted light makes an angle of 42 degress, what is the critical angle for light incicdent on the same boundary.
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Explanation / Answer
1. a light spring with spring constant 1200 n/m has a 55g object at its end. (a) If the energy of the system is 6.0J what is the amplitude of the vibration? (b) What is the maximum speed of the object? (C) What is the speed when the object is at a position x= A/2? What assumptions did you make? Answer : a) K = 1200 N/m m = 55 g = 0.055g Energy of the system = 6 J = 0.5 KA^2 Hence, x = sqrt (6/0.5*1200 ) = 0.1 m is Amplitude b) maximum speed : 0.5mv^2 = 6J v = sqrt (6 / 0.5*0.055) = 14.77 m/s c) when object is at position A/2 = 0.05: 0.5kx^2 = 0.5mv^2 1200*0.05^2 = 0.055 v^2 v = 7.385 m/s 2. Determine the frequency of vibration for an spring mass system that has a mass of 100 grams a spring constant of 20 N?m and the distance from the +A to -A is 0.40m . Determine the maximum speed of the System Assuming the period is the same for the pendulum determine the pendulum length w = sqrt(k/m) = sqrt(20/0.1) = sqrt(200) = 14.14 rad/s f = w/2pi = 2.25 Hz ; 0.5*m*v^2 = 0.5*k*A^2 m =0.1 k = 20 A = 0.4/2 = 0.2 v(max) = 2.828 m/s T= 1/f = 4/9 T = 2*pi sqrt(l/g) L = 0.049 m 3. Answer : lamda = velocity/frequency = 3/2 = 1.5 m Wavelength is the answer for this question ; as distance between two peaks is equal to wavelength 4. A wooden flute open at both ends is 0.48 m long (a) Determine its fundamental vibration frequency, (b) How far from one end should a finger hole be placed to produce a sound whose frequency is four thirds that calculated in part (a) . What Assumptions are there in this? a) fo = v/(2L) = 343/(2*0.48) = 357.29 Hz b) f = 476.388 fo = v/(2L) L = 0.36 m 5. Light is an incident on the boundarybetween 2 media at an angle of 32 degrees. If the refracvted light makes an angle of 42 degress, what is the critical angle for light incicdent on the same boundary. n1* sin 32 = n2* sin 42 n2/n1 = 0.7919 sin theta = 0.7919 theta = 52.368 degrees Please rate only the complete answer
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