are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance from 0 is r

1. The oscillation of rod OA about 0 is defined by the relation B

-sinnt

, where 0

;rd

and

are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance from 0 is r

x, where r and r are expressed in mm and

t i - 6

seconds, respectively. When t

Is, determine

(a) The velocity of the collar.

(b) The acceleration of the 'collar.

(c) The acceleration of the collar relative to the rod.

2.

The circular plate shown rotates about its vertical diameter at the constant rate ol=10 radls. Knowing that in the position shown the disk lies in the XY plane and point D of strap CD moves upward at a constant relative speed u=1.37m/s,

determine

(a) The velocity of

D.

(b) The acceleration of D.

0"

S

Pro. 2

3.

Two swimmers A and By of mass 75 kg and 50 kg, respectively, dive off the end of a 200-kg boat. Each swimmer has a relative horizontal velocity of 3

leaving the boat. If the boat is initially at rest, determine its final velocity, assuming that

(a) The two swimmers dive simultaneously.

(b) The swimmer A dives first and then B. (7%)

(c) The swimmer B dives first and then A. (7%)

Pro. 3

4. The collar B of negligible mass can slide freely on the 4-kg uniform rod CD.

Knowing that in the position shown crank AB rotates with an angular velocity of 5 radls and an angular acceleration of 60 rad/s2.

(a) If both angular velocity and angular acceleration is clockwise, determine the

force exerted on rod CD by collar B. (7%)

(b) If both angular velocity and angular acceleration is counterclockwise, determine the force exerted on rod CD by collar B.

Pro. 4

5 .

A 7.5-kg slender rod AB is riveted to a 6-kg uniform disk as shown. A belt is attached to the rim of the disk and to a spring which holds the rod at rest in the position. If end A of the rod is moved 20 mrn down and released, determine

(a) The period of vibration. (8%)

(b) The maximum velocity of end A.

Pro. 5

6. The 18-kg rigid body BD consists of two identical 6-cm-radius spheres and the rod which connects them and has a centroidal radius of gyration of 25.4 cm. The body is at rest on a horizontal frictionless surface when it is struck by the 6-kg sphere A which has a radius of 6 cm and is moving as shown with a velocity

of magnitude 3.7 mls, Assuming a perfectly plastic impact, determine immediately after the impact,

(a) The angular velocity of body BD.

(b) The velocity of point G

Pro. 6