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ENGGEN 121 Engineering Mechanics
Dynamics Test
Time allowed: 1 hour
Attempt ALL four questions, each carry equal marks
Write your final answers in the boxes provided on the question pages.
Use blue or black ink. Pencil is accepted for drawing diagrams.
The work justifying your answer must be shown on the relevant pages. If there is not
enough space for your working, you may continue on the back of the page, but PLEASE PUT
A TICK in the box provided.
The following may be used in the examination:
• Restricted calculators
• One A4 note sheet. The note sheet must be hand written in English and must not contain
any worked examples. You will be required to submit your note sheet with the test script.
Marks:
Q1
Q2
Q3
Q4
Total /40
Vexit = Shalf = thalf =
Tick box if solution
continued next page
Question 1
A rail gun uses electromagnetic force to launch a
projectile at a high velocity. An acceleration
profile of a projectile fired from a rail gun is
presented on the right. The projectile leaves the
rail gun barrel 0.08 s after being fired (t = 0 s),
and hits a target at 1.5 s before coming to a
complete stop inside the target. The diagram is
not drawn to scale. Assume effects of air drag and
gravity to be negligible.
(a) The projectile is initially at rest, and experiences a constant acceleration of 3800 times
Earth’s gravity while it is inside the barrel. What is the exit speed Vexit of the projectile
as it leaves the barrel?
(b) Once the projectile hits the target, it experiences deceleration of a = -0.167 v2 m/s2,
where v is the speed of the projectile in m/s. Find the distance the projectile travels
inside the target while the speed of the projectile is halved, Shalf. Assume the projectile
continue on a linear path.
(c) What is the time taken for the projectile to reduce its speed by half (thalf) since it entered
the target?
N = atotal = VW =
Tick box if
solution continued
next page
Question 2
A rollercoaster cart of mass = 800 kg (including
passengers) is going through a vertical loop track.
The velocity of the cart at A is 45 km/h, and the
radius of the loop r is 18 m. The angle θ is 35°. The
dynamic frictional coefficient is k = 0.14. If the cart
can be treated as a particle, determine the following
for point A:
(a) Magnitude and direction of the normal force
N required.
(b) Determine the magnitude and direction of total acceleration of the rollercoaster cart at
position A.
(c) A person sitting in the cart will feel the sensation of increased or reduced weight due to
the normal support force, N. For a person sitting in the cart to feel ‘weightless’ at point
A, what should be the speed of the cart, VW be?
(b) (c) aC =
Tick box if solution
continued next page
Question 3
Consider the pulley system shown on the right.
Mass of block A is half of block B, and blocks A and
C have the same mass. The cable is rigid and has
negligible mass and the pulleys are frictionless.
(a) Draw free body diagrams of each mass.
(b) Determine the kinematic constraint
equation for the acceleration of the masses.
(c) What is the acceleration of mass C? In
which direction?
tfall= Smax =
Tick box if solution
continued next page
Question 4
A flagpole is falling to the ground due to a strong wind
and has a constant angular acceleration of 0.7 rad/s2
(CW). At the instant shown, the angular velocity of the
pole is 1.3 rad/s (CW). At the same instant, a person is
running towards the flagpole to secure it, travelling 1.5
m/s with a constant acceleration of 1.8 m/s2. The
diagram is not drawn to scale. For the instant,
determine:
(a) Draw the acceleration diagram of the point G and the person.
(b) How long would it take for the pole to fall to the ground from the current position?
(c) What is the maximum distance the person can cover to reach the point G before the pole
hits the ground?