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can u give detail for calculation please, some calculations I stuck

can u give detail for calculation please, some calculations I stuck

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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can u give detail for calculation please, some calculations I stuck

/2ga sin 0 i.c. angular velocity, w = k + a² do Angular acceleration dt do do OP 2ga do dt (2ga sin 0\- 12 + a² (2ga sin 6' k² + a² /½ = }.x cos 0 x 12 + a² gа cos 0 k² + a² `R C.F. ng b) When the plank has turned through an angle as in the above Figure, the force acting along the plank is the sum of the centrifugal force and the com- ponent of the weight parallel to the plank. i.e. tangential force, F = mo²a + mg sin a 2ga sin a = m.- a + mg sin a 1:2 + a² 1:2 + 3a? = mg sin a. k2 + a? The normal reaction, R, is given by do Ra = I dt mk2 ga cos a * 1:² + a² k* cos a i.e. R= mg 1k² + a² mg sin a F k2 + 3a* k² + a² k2 + 3a? tan a R k2 cos a mg 7:2 + a²
Transcribed Image Text:/2ga sin 0 i.c. angular velocity, w = k + a² do Angular acceleration dt do do OP 2ga do dt (2ga sin 0\- 12 + a² (2ga sin 6' k² + a² /½ = }.x cos 0 x 12 + a² gа cos 0 k² + a² `R C.F. ng b) When the plank has turned through an angle as in the above Figure, the force acting along the plank is the sum of the centrifugal force and the com- ponent of the weight parallel to the plank. i.e. tangential force, F = mo²a + mg sin a 2ga sin a = m.- a + mg sin a 1:2 + a² 1:2 + 3a? = mg sin a. k2 + a? The normal reaction, R, is given by do Ra = I dt mk2 ga cos a * 1:² + a² k* cos a i.e. R= mg 1k² + a² mg sin a F k2 + 3a* k² + a² k2 + 3a? tan a R k2 cos a mg 7:2 + a²
Figure Q7 shows a uniform plank, rests upon a horizontal bench with one end of the bar projecting over the sharp edge of the bench, the bar being at right angles to this edge. The plank is pulled out of horizontally until the centre of gravity overhangs the edge by a distance a, and is then released. The plank rotates about the edge and then slides down. (a) Determine the angular velocity and angular acceleration of the plank after it has turned through an angle O degrees assuming that no sliding has taken place. (b) If the sliding begins when the plank has tuned through an angle a, show that the coefficient of friction, u , is [(k? + 3a?) ------------- tan a. k? where k is the radius of gyration of the plank about its centre of gravity. a Figure Q7, A uniform plank resting upon a horizontal bench. Solution (a) When the plank has rotated through an angle 0, loss in P.E. = gain in K.E. m(k² + a²)w2 |3D i.e. mga sin 0
Transcribed Image Text:Figure Q7 shows a uniform plank, rests upon a horizontal bench with one end of the bar projecting over the sharp edge of the bench, the bar being at right angles to this edge. The plank is pulled out of horizontally until the centre of gravity overhangs the edge by a distance a, and is then released. The plank rotates about the edge and then slides down. (a) Determine the angular velocity and angular acceleration of the plank after it has turned through an angle O degrees assuming that no sliding has taken place. (b) If the sliding begins when the plank has tuned through an angle a, show that the coefficient of friction, u , is [(k? + 3a?) ------------- tan a. k? where k is the radius of gyration of the plank about its centre of gravity. a Figure Q7, A uniform plank resting upon a horizontal bench. Solution (a) When the plank has rotated through an angle 0, loss in P.E. = gain in K.E. m(k² + a²)w2 |3D i.e. mga sin 0
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