0.32 m/s and is found to take 48 s to completely encircle the hive 5 times. (a)
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Question
0.32 m/s and is found to take 48 s to completely encircle the hive 5 times. (a) What is the period of the bee's circular motion? (b) What is the linear frequency of the bee's motion? (c) What is its angular frequency? (d) What is the radius of the circular motion about the hive? Some Standards 2. An old record is spinning on an equally old turntable at 78 rpm (revolutions per minute). Answer all of the questions below in MKS units. (a) How many times does the record rotate per second? (b) What is the angular frequency of the record? (c) How long does it take the record to complete one revolution? (d) What is the speed of a dust particle stuck to the record at a point which is 4 inches from the record's axis of rotation? (e) What is the centripetal acceleration of the dust particle mentioned above? 3. A 400 -kg plane is flying in a horizontal circle of radius 1.3 km. In order to make the turn, the plane is banking at an angle of 20deree. (That is, it is tilted from its horizontal position by 20 degree .) The lift force L provided by the wings acts as a kind of normal force which acts in the direction shown below (perpendicular to the wings). Ignore any frictional effects in this problem. (a) What is the magnitude of the lift force provided by the plane's wings? (Hint: Look at the sum of forces in the vertical direction. What is the acceleration of the plane in the vertical direction? Is it even moving in the vertical direction?) (b) With what constant speed must the plane be flying? (Hint: What's the equation for the centripetal acceleration? Look at Newton's 2nd law applied to the c -direction!)Explanation / Answer
2.
78rpm = 78r/60s = 1.3rotations/sec
Angular frequency = rps*2*pi = 8.16 rad/s
TIme to complete one revolution = 2pi/8.16 = 0.77s
Speed of dust particle = r*angular freq. = 4*8.16 =32.6 in/s = 0.828m/s
centrepetal acceleration = V^2/r = 266.3 in/s2 = 6.74m/s2
3.
Balance vertical forces
L*cos20=mg = 3924N => L = 4176N
Balance horizontal forces
L*sin20 provides centrefugal force mV^2/R
L*sin20=400V^2/1300 => V = 68.13m/s
Acceleration of plane in vertical direction = 0 because lift balances gravitational force otherwise it wont be able to make a horizontal circle as stated inthe question.
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