dynamics

UEME 1143 – 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 𝐼 = 1

12 𝑚𝑙2.

(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