UEME 1143 โ Dynamics
Assignment 2
Instructions:
Answer ALL questions and submit your answers in softcopy only (PDF format) using the
Assignment 2 Submission Link in wble before the due date. The answer can be in either hand
writing or computer typing but make sure it is clear enough to be read! Also, include the
given cover page in your submission.
Q1. A 10 g bullet travels at a horizontal velocity of 200 m/s and bombards the lower end
of a stationary bar of mass m = 0.5 kg and length l = 500 mm, as shown in Figure Q1.
The bullet is imbedded to the bar after the impact. The moment of inertia of the bar is
given as ๐ผ =
1
12
๐๐2.
(i) Draw the impulse-momentum diagram of the entire system before and after
the impact. (5 marks)
(ii) Determine the required distance h if the impulsive reaction at C is zero.
(12 marks)
(iii) Determine the corresponding angular velocity of the bar immediately after the
arrow strikes and becomes embedded in the bar. (8 marks)
[Total: 25 marks]
Figure Q1
200 m/s
h
A
B
C
L = 500 mm
Q2. You are required to propose the intermediate four (4) sections of a track with sphere
rolling on it as indicated in Figure Q2. There are no restrictions on the dimensions
(length, height, etc) for the four sections. A sphere of mass 1kg and radius of 10cm is
to be released from rest at point A, then rolls without sliding on the track including the
four sections that you proposed. At the last section of the track, the sphere is moving
on a horizontal surface and reaches point B where it leaves the surface and travel
towards point C. Knowing that a = 1m, b=2m.
As part of requirements, the four sections of the track should have:
1. At least two (2) sections of curve (any radius of your choice)
2. Incline or decline surface(s) (any length or angle of your choice).
Sketch the proposed track with proper labelling and dimensioning.
(i) Select a method to solve this question and explain on your selection.
(5 marks)
(ii) With the method selected in Part (i), determine the velocities at the starting
and ending points of each section for the proposed track. (10 marks)
(iii) Determine the distance travelled (c) based on your proposal. (5 marks)
(iv) Explain with calculations on what modification(s) that you can later propose
to further increase the distance travel (c). (5 marks)
[Total: 25 marks]
Figure Q2
1 2 3 4