Dynamics Sample Test 3

Dynamics Sample Test 3
1. Two blocks and a pulley are connected by inextensible cords.
Block A has a constant acceleration of 75 mm/s2 and an initial
velocity of 120 mm/s, both directed downward. Determine
a) the number of revolutions executed by the pulley in 6 seconds,
b) the velocity of B after 6 seconds,
c) the acceleration of point C on the rim of the pulley at t=0.
Answers:
a) 1.647 rev
b) 256 mm/s
c) 104.0 mm/s2
2. At the instant shown, bar AB has a
counterclockwise angular velocity of 2 rad/s.
Determine the angular velocities of bars BC and
CD.
Answer: ωBC = 2 rad/s ccw; ωCD = 7 rad/s cw
3. At the instant shown, bar AB has a constant
counterclockwise angular velocity of 2 rad/s.
Determine
a) the angular velocities of bars BC and CD
b) the angular accelerations of bars BC and
CD.
Answer: ωBC = 2 rad/s ccw; ωCD = 7 rad/s cw
3. At the position shown bar AB has an angular
velocity of ωAB = 2 rad/s, and an angular
acceleration of αAB = 4 rad/s2 , both
counterclockwise. Block C is constrained to
move along the horizontal. Determine
a. the angular acceleration of bar BC,
b. the acceleration of block C.
Answers: αBC = 1.8475 rad/s2 ccw; ac = 16.906 to
the left
4. At the position shown bar AB has an angular
velocity of ωAB = 2 rad/s, and an angular
acceleration of αAB = 4 rad/s2 , both
counterclockwise. Block C is constrained to
move along the horizontal. Determine
c. the angular acceleration of bar BC,
d. the acceleration of block C.
Answers: αBC = 1.8475 rad/s2 ccw; ac = 16.5625
to the left
SOLUTION USING VECTORS:
4. Bar AC has a counterclockwise angular velocity
ωAC = 2 rad/s, and a clockwise angular
acceleration αAC = 4 rad/s2 . The pin at C slides in
the slot in bar BD.
a. Determine the angular velocity of bar BD and
the velocity of the pin relative to the slot.
b. Determine the angular acceleration of bar BD
and the acceleration of the pin relative to the
slot.
Answers: ωBD = 2 rad/s ccw; vc/F = 14 in/s; αBD =
11 rad/s2 cw; aC/F = 28 in/s2 downward.