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Eastern Mediterranean University

Faculty of Engineering

Department of Mechanical Engineering Rigid Body Dynamics - MENG233 (Assignment 2)

Instructors: (Please select and tick the name of your related lecturer)

Group 1: Prof. Dr. Fuat Egelioğlu

Group 2: Assoc. Prof. Dr. Qasim Zeeshan

Student’s Name and Surname:

……………………………….

Student Number: ………………………………

ASSIGNMENT 2

DUE DATE: 29 DEC 2016 -------------------------------------------------------------------------------

Instructions: 1. Answers are to be written in the spaces provided under each question.

Questions Marks Questions Marks

1 11

2 12

3 13

4 14

5 15

6 16

7 17

8 18

9 19

10 20

21

22

23

24

25

TOTAL

2

1. Each ball has a mass m and the coefficient of restitution between the balls is e. If

they are moving towards one another with a velocity , determine their speeds after

collision. Also, determine their common velocity when they reach the state of

maximum deformation. Neglect the size of each ball.

3

2. A man hits the 50-g golf ball such that it leaves the tee at an angle of 40° with the

horizontal and strikes the ground at the same elevation a distance of 20 m away.

Determine the impulse of the club C on the ball. Neglect the impulse caused by the

ball’s weight while the club is striking the ball.

4

3. If it takes 35 s for the 50-Mg tugboat to increase its speed uniformly to 25 km/hr

starting from rest, determine the force of the rope on the tugboat. The propeller

provides the propulsion force F which gives the tugboat forward motion, whereas

the barge moves freely. Also, determine F acting on the tugboat. The barge has a

mass of 75 Mg.

5

4. The train consists of a 30-Mg engine E, and cars A, B, and C, which have a mass of

15 Mg, 10 Mg, and 8 Mg, respectively. If the tracks provide a traction force of F =

30 kN on the engine wheels, determine the speed of the train when t = 30 s ,

starting from rest. Also, find the horizontal coupling force at D between the engine

E and car A. Neglect rolling resistance.

6

5. The tennis ball is struck with a horizontal velocity VA strikes the smooth ground at

B, and bounces upward at = 30 deg. Determine the initial velocity VA the final

velocity VB and the coefficient of restitution between the ball and the ground.

7

6. Two smooth disks A and B each have a mass of 0.5 kg. If both disks are moving

with the velocities shown when they collide, determine the coefficient of restitution

between the disks if after collision B travels along a line, 30° counterclockwise

from the y axis.

8

7. The car A has a weight of 4500 lb and is traveling to the right at 3 ft/s. Meanwhile

a 3000-lb car B is traveling at 6 ft/s to the left. If the cars crash head-on and

become entangled, determine their common velocity just after the collision.

Assume that the brakes are not applied during collision.

9

8. The cue ball A is given an initial velocity (vA)1 = 5 m/s. If it makes a direct

collision with ball B (e = 0.8), determine the velocity of B and the angle just

after it rebounds from the cushion at C (e’ = 0.6). Each ball has a mass of 0.4 kg.

Neglect the size of each ball.

10

9. Two identical cars A and B are at rest on a loading dock with brakes released. Car

C, of a slightly different style but of the same weight, has been pushed by

dockworkers and hits car B with a velocity of 1.5 m/s. Knowing that the coefficient

of restitution is 0.8 between B and C and 0.5 between A and B, determine the

velocity of each car after all collisions have taken place.

11

10. An amusement park ride consists of a car which is attached to the cable OA. The

car rotates in a horizontal circular path and is brought to a speed v1 = 4 ft/s when

r= 12 ft . The cable is then pulled in at the constant rate of 0.5 ft/s. Determine the

speed of the car in 3 s.

12

11. The disk is originally rotating at 0 = 8 rad/sec. If it is subjected to a constant

angular acceleration of = 6 rad/sec2. determine the magnitudes of the velocity

and the n and t components of acceleration of point B just after the wheel

undergoes 2 revolutions.

13

12. The vertical-axis windmill consists of two blades that have a parabolic shape. If the

blades are originally at rest and begin to turn with a constant angular acceleration

of c = 0.5 rad/s2, determine the magnitude of the velocity and acceleration of

points A and B on the blade when t=4 s.

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13. A motor gives gear A an angular acceleration of A =(4t3) rad/s

2,

where t is in seconds. If this gear is initially turning at (A)0 = 20 rad/s,

determine the angular velocity of gear B when t = 2 s.

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14. The operation of “reverse” for a three-speed automotive transmission is illustrated

schematically in the figure. If the crank shaft G is turning with an angular speed of

60 rad/s, determine the angular speed of the drive shaft H. Each of the gears rotates

about a fixed axis. Note that gears A and B, C and D, E and F are in mesh. The

radii of each of these gears are reported in the figure.

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15. Rotation of the robotic arm occurs due to linear movement of the hydraulic

cylinders A and B. If this motion causes the gear at D to rotate clockwise at 5 rad/s,

determine the magnitude of velocity and acceleration of the part C held by the grips

of the arm.

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16. The shaper mechanism is designed to give a slow cutting stroke and a quick return

to a blade attached to the slider at C. Determine the velocity of the slider block C at

the instant ɵ = 60°, if link AB is rotating at 4 rad/s.

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17. The crankshaft AB is rotating at a constant angular velocity of =150 rad/s .

Determine the velocity of the piston P at the instant = 30°.

19

18. If the block at C is moving downward at 4 ft/s, determine the angular velocity of

bar AB at the instant shown.

20

19. The crankshaft AB turns with a clockwise angular velocity of 10 rad/s, Fig.

Determine the velocity of the piston at the instant shown

21

20. The 2-Mg truck achieves a speed of 15 m/s with a constant acceleration after it has

traveled a distance of 100 m, starting from rest. Determine the normal force exerted

on each pair of front wheels B and rear driving wheels A. Also, find the traction

force on the pair of wheels at A. The front wheels are free to roll. Neglect the mass

of the wheels.

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21. As the car travels forward at 80 ft/s on a wet road, due to slipping, the rear wheels

have an angular velocity = 100 rad/s. Determine the speeds of points A, B, and C

caused by the motion.

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22. Crank AB rotates with the angular velocity and angular acceleration shown.

Determine the acceleration of the slider block C at the instant shown.

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23. A uniform rectangular plate has a mass of 5 kg and is held in position by three

ropes as shown. Knowing that ɵ = 30°, determine, immediately after rope CF has

been cut, (a) the acceleration of the plate, (b) the tension in ropes AD and BE.

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24. The thin plate ABCD of mass 8 kg is held in the position shown by the wire BH

and two links AE and DF. Neglecting the mass of the links, determine immediately

after wire BH has been cut (a) the acceleration of the plate, (b) the force in each

link.

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25. Three bars, each of mass 3 kg, are welded together and pin-connected to two links

BE and CF. Neglecting the weight of the links, determine the force in each link

immediately after the system is released from rest.