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MEC420: Dynamics (October 24 – January 25 ) Group Assignment No. Student ID Name Marks:
Group: This is a group work assignment (max 3 students/group) Due Date: 24 / 1 / 2025 ( 05 : 00 PM). Late submission will be penalised. Total Instruction:
1. Solution MUST include all free-body and kinetics diagrams, calculations, plots, assumptions, and justification, as deemed necessary. Marks will be awarded or deducted accordingly. [60% marks will _be awarded to the solution].
- Briefly describe the steps of your solutions, such as the fundamental and dynamics formula applied_ _and their justifications. [30% marks will be awarded to your efforts].
- This assignment shall be submitted in a report format with good and neat presentation. Attention shall_ be especially given to units, vector writing and labelling your answer. [10% marks will be awarded to _your submission & presentation].
- All answers shall be submitted together as a report in hardcopy to my office at_ T1-A1 1 - 4C. QUESTION 1 (a) Explain all the possible types of accelerations in kinematics of particles and graphically show how they are related with the velocities. (CO1/C2/5 marks) (b) Pin A moves down the fixed parabolic shaft at a constant speed of v = 20 cm/s, driven by the slotted arm OB which is rotating about a fixed axis through O as shown in Figure Q1. At the instant shown, when the angle θ is 40°, the position x of pin A is 30 cm from fixed origin C. Given that the shape of the parabolic shaft is described by the equation y = 0.05 x^2 (in cm) and the length L = 40 cm, determine (i) the acceleration of the pin A , (ii) the angular velocity of the slotted arm OB , 𝜃̇ , (iii) the angular acceleration of the slotted arm OB , 𝜃̈ , (iv) the relative velocity of the pin A with respect to the slotted arm OB , 𝑟̇ , and (v) the relative acceleration of the pin A with respect to the slotted arm OB , 𝑟̈. (CO2/C4/12 marks) (c) Evaluate at the same instant, the effect on the speed of pin A if the angular speed of the slotted arm OB is greater. (CO3/C6/3 marks)
Figure Q
O
A
B
θ L
D
y x 30
C
(a) With the aids of diagrams and equations, compare and contrast the principle of work and energy, impulse and momentum method and equation of method in kinetic analysis of particles. (CO1/C2/5 marks) (b) Figure Q 3 shows a motor C used to control the motion of blocks A and B , each of mass 2 0 kg and 10 0 kg,
respectively, where = 30º. The system is at rest when the motor suddenly applies a constant force F on
block A causing block B to slide up the frictionless incline surface. (i) Draw the free-body and kinetic diagrams of each block. (ii) Write the equations of motion of each block. (iii) Determine the applied force F required to give the block B an acceleration of 2 m/s^2 immediately after block A is being pulled by the motor and the corresponding tension in the cable. (CO2/C4/12 marks) Figure Q (c) Evaluate the applied force required if the block B and the incline surface had a certain coefficient of friction μ. Justify your answer by means of formulation used in Q 3 (b). (CO3/C6/3 marks)
B
C
θ
A
y x
(a) Briefly describe with the aids of diagrams the principle of work and kinetic energy and the conservation of energy methods in kinetics analysis of particles. (CO1/C2/5 marks) (b) In the position shown in Figure Q 4 , the spring of stiffness k = 1.5 kN/m is being compressed by 0.2 m
when the mechanism is released from rest at = 20º. The mass of each sphere A and sphere B is 5 kg and
3 kg. Ignoring the mass of the arms and knowing that the lengths of arm OA and arm OB are 0. 15 m and 0.3 m, respectively, determine
(i) the angular velocity of the arm when = 0º,
(ii) the velocities of sphere A and B , and
(iii) the maximum angle reached by the arm.
(CO2/C4/12 marks) Figure Q (c) Upon reaching the horizontal position (i.e. = 0), the spring is removed by a quick-release mechanism. Evaluate the motions of sphere A and B. Justify your answer using dynamics fundamentals. (CO3/C6/3 marks) θ
B
A
C
O
0.3 m
(a) Briefly describe with the aid of diagrams the general plane motion of a rigid body by giving an example of its application in automotive engineering. (CO1/C2/5 marks) (b) In the mechanism shown in Figure Q 6 , the wheel of radius r 1 = 3 5 cm is driven to roll without slipping to the left by the rolling motion of a larger wheel. The larger wheel of radius r 2 = 4 5 cm rotates at a constant
angular speed of = 10 rad/s in counter-clockwise direction. Knowing that the length of link AB is 80
cm, determine when = 30 º
(i) the velocity the point A , (ii) the angular velocity of link AB , (iii) the angular velocity of the wheel of radius r 2 , (iv) the velocity of points B and C , and (v) the relative velocity of point A with respect to point C. (CO2/C4/12 marks) Figure Q 6 (c) Evaluate the effect of angular speed Ω of the larger wheel on the velocity of point A. Justify your answer by using the analysis used in Q 6 (b). (CO3/C6/3 marks)
C
A
B
θ r 2 r 1
y x θ
(a) Briefly describe with the aid of diagrams how the principle of work and energy is applied in kinetics analysis of rigid bodies by giving an example of application. (CO1/C2/5 marks) (b) The circular plate of radius r = 500 mm shown in Figure Q 7 is pivoted at fixed point O. The circular plate is released from rest at the position when θ = 30°. Given that the mass of the circular plate is 3 kg, determine (i) the angular acceleration of the circular plate immediately after it is released, (ii) the force reaction at pivot O immediately after the circular plate is released, (iii) the angular velocity of the circular plate when θ = 6 0°, and (iv) the velocity of point A when θ = 6 0° (CO2/C4/12 marks) Figure Q (c) Evaluate the effect on the angular speed of the circular plate when θ = 6 0° if a frictional moment was to be exerted at the pivot O. Justify your answer by using the analysis used in Q 7 (b). (CO3/C6/3 marks) θ
O
G
r A
(a) Using the mechanical system shown in Figure Q 7 , with the aid of diagrams, describe the rotation about a fixed point by clearly showing with proper labels, the centre of rotation, all the axes of rotation, the instantaneous axis of rotation, the space and body cones and the angular velocity and acceleration of the rotating body. (CO1/C2/5 marks) (b) At the instant shown in Figure Q7 , cone B is rolling without slipping around the fixed cone A with a constant angular velocity = 15 rpm. Given the height of cone B is 800 mm and radii of cone A and cone B are 320 mm and 200 mm, respectively, determine i. the absolute angular velocity and acceleration of cone B ii. the velocity and acceleration of point P. (CO2/C4/12 marks) (c) While cone B dimensionally remains the same, evaluate the effect smaller radius of cone A on the velocity of point P. Justify your answer by using analysis used in Q 7 (b). (CO3/C6/3 marks) Figure Q 7
