4400

Semester 2 2008

The University of Sydney Faculty of Engineering

AMME1550 Dynamics 1

All questions are to be answered. All questions are of equal value.

Time Allowed: 3 hours

This is an open book examination. All material, including lecture notes, text books, and electronic calculators, are allowed in the examination room.

Question 1 (25%)

Gas guns are used to investigate the properties of materials SUbjected to high velocity impacts. A projectile is accelerated through the barrel of the gun by gas at high pressure. Assume that the acceleration of the projectile in mls2 is given by a = c / s, where s is the position ofthe projectile in the barrel in meters and c is a constant that depends on the initial gas pressure behind the projectile. The projectile starts from rest at s = 1.5 m and accelerates until it reaches the end of the barrel at s = 3 m. Determine the value of the constant c

necessary for the projectile to leave the barrel with a velocity 0[200 mls.

~(:.~- - ...... ',.~ ..... ::' .. ,.. ., - -I---s - ----1

Question 1

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4400 Semester 2 2008 Page 2 of3

Question 2 (25%)

The smooth circular bar rotates with constant angular velocity 000 about the vertical axis AB. The radius R = 0.5 m. The mass m remains stationary relative to the circular bar at f3 = 40°. Determine 000 •

A

Question 2

Question 3 (25%)

The spring constant k = 700 N /m. The masses rnA = 14 kg and rnB = 18 kg. The horizontal bar is smooth. At the instant shown, the spring is unstretched and the mass B is moving downwards at 1 mls. How fast is B moving when it has moved downward 0.2 m from its present position?

Question 3

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4400 Semester 2 2008 Page 3 of3

Question 4 (25%)

The bar rotates in the horizontal plane about a smooth pin at the origin. The 2-kg sleeve A slides on the smooth bar, and the mass of the bar is negligible in comparison to the mass of the sleeve. The spring constant is k = 40 N/m , and the spring is unstretched when r = O. At t = 0, the radial position of the sleeve is r = 0.2 m and the angular velocity of the bar is 000 = 6 rad/s. What is the angular velocity of the bar whenr = 0.25 m?

Question 4

This is the end of your questions.

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