A flea is at point A on a horizontal turntable 10.7 cm from the center. The turn

Question

A flea is at point A on a horizontal turntable 10.7 cm from the center. The turntable is rotating at 36.2 rev/min in the counterclockwise direction. The flea jumps vertically upward to a height of 5.28 cm and lands on the turntable at point B. Place the coordinate origin at the center of the turn table with the positive x axis fixed in space and initially passing through A. The acceleration of gravity is 9.8 m /s2. Find the linear displacement of the flea. Answer in units of m. Find the angle through which point A has rotated when the flea lands. Answer in units of degree. Find the distance of point B from the origin when the flea lands. Answer in units of m. What angle does the radius drawn through B make with the x-axis when the flea lands? Answer in units of degree. What is the linear speed of the flea after it lands? Answer in units of m/s.

Explanation / Answer

The angular speed of the turn table is w = 36.2 rev/min
= 36.2*2(pi)/60 rad/s
= 3.79 rad/s
The initial position of the flee is x0 = 10.7 cm from the origin Let the initial position be at A The flee jumps to a height h = 5.28 cm = 0.0528 m The initial velocity of the flee can be written as u = sqrt(2gh)                                                                          = sqrt(2*9.8*0.0528)                                                                          = 1.017 m/s The time taken by the fleee to land on the table T = 2*u/g                                                                          = 2*1.017/9.8                                                                          = 0.207 s The angular displacement of the turntable is theta = wT                                                                          = 3.79*0.207                                                                          = 0.785 rad As the flee jumps vertically, again it lands at, B, the same point i.e 10.7 cm distance from the origin. The horizontal displacement og the point A from the centre after the flee lands is given by x' = x0 cos(theta)         = 10.7 cos (0.785 rad)         = 7.57 cm 005) The linear displacement of the flee is given by d = x0-x'                                                                        = 10.7 - 7.57                                                                        = 3.13 cm 006) The angle through which the point A rotated is theta = 0.785 rad                                                                              = 0.785*360/2(pi)                                                                              = 45 degree 007) As the flee jumps vertically, again it lands at, B, the same point i.e 10.7 cm distance from the origin. 008) The angle made by the radius drawn from B makes an angle 45 degree with the X axis in clockwise direction 009) The linear velocity of the flee v = linear displacement / time                                                = 3.13 cm / 0.207 s                                                = 0.15 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.