Tutorial (2) Subject: Curvilinear Motion A Cartesian Coordinates

Transcription

1 Faculty of EMS Department: Mechatronics Course : MECHANICS II Prof. Dr. E. I. Morgan Tutorial () Subject: Curvilinear Motion A Cartesian Coordinates Prob. 1: [11.98] While delivering newspapers, a girl throws a paper with a horizontal velocity v o. Determine the range of values of v o if the newspaper is to land between points B and C. Answer : 4.87m/ s vo 11.44m/ s - 1 -

2 Prob. : [11.10] Water flows from a drain spout with an initial velocity of 0.76 m/s at an angle of 15 o with the horizontal. Determine the range of values of the distance d for which the water will enter the trough BC. 0 d

3 Prob. 3: [11.105] A homeowner uses a snow blower to clear his drive way. Knowing that the snow is discharged at an average angle of 40 o with the horizontal, determine the initial speed v o of the snow. vo 6.98m / s - 3 -

4 Prob. 4: [11.106] A basketball player shoots when she is 5 m from the backboard. Knowing that the ball has an initial velocity v o at an angle of 30 o with the horizontal, determine the value of v o when d is equal to (a) 8 mm, (b) 430 mm. a) v b) v o o 9.34m/ s 9.7m/ s - 4 -

5 B Intrinsic Coordinates Prob. 5: [11.135] Determine the maximum speed that the cars of the roller-coaster can reach along the circular portion AB of the track if the normal component of their acceleration cannot exceed 3g. v max 97.6km/ h - 5 -

6 Prob. 6: [11.137] Pin A, wich is attached to link AB, is constrained to move in the circular slot CD of radius R = 0.9 m. Knowing that at t = 0 the pin starts from rest and moves so that its speed increases at a constant rate of 0.0 m/s, determine the magnitude of its total acceleration when: (a) t = 0, (b) t = s. a) a b) a A A 0.0m / s 0.0m / s R - 6 -

7 Prob. 7: [11.140] A motorist starts from rest at point A on a circular entrance ramp when t = 0, increases the speed of her automobile at a constant rate and enters the highway at point B. Knowing that her speed continues to increase at the same rate until it reaches 100 km/h at point C, determine: (a) the speed at point B, (b) the magnitude of the total acceleration when t = 0 s. v B 83.8km/ hr a 3.71m / s - 7 -

8 Prob. 8: [11.143] A projectile is launched from point A with an initial velocity v o of 40 m/s at an angle of 30 o with the vertical. Determine the radius of curvature of the trajectory described by the projectile (a) at point A, (b) at the point B on the trajectory where the velocity is parallel to the incline. 36m A 6.8m B - 8 -

9 C Polar Coordinates Prob. 9: [11.161] The rotation of rod OA about O is defined by the relation θ = 0.5e - 0.8t sin 3πt, where θ and t are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance from O is: r = t 6.7t + 6.4t 3, where r and t are expressed in meters and seconds, respectively. When t = 0.5 s, determine: (a) the velocity of the collar, (b) the acceleration of the collar, (c) the acceleration of the collar relative to the rod. a) v r b) a r 0, v 5.74m/ s, a m/ s [ v 8.8m/ s c) relative acc.? 5.76m/ s tot? mag. & dir.] [ a tot? mag.& dir.] - 9 -

10 Prob. 10: [11.164] The path of a particle P is a limacon. The motion of the particle is defined by the relations: r = b ( + cos πt) and θ = πt where t and θ are expressed in seconds and radians, respectively. Determine: (a) the velocity and the acceleration of the particle when t = s, (b) the value of θ for which the magnitude of the velocity is maximum. a) v 3 beˆ a 4 beˆ b) N, N r 0,1,,... 10

11 Prob. 11: [11.170] Pin C is attached to rod BC and slides freely in the slot of rod OA. Rod BC rotates at the constant rate ω. At the instant when β = 60 o determine: (a) r and, (b) r and. Express your answers in terms of d and. Note that: 1 1 a) r d, b) r 3 4 d, 0 ω 11