課程名稱︰動力學
課程性質︰機械系必修
課程教師︰顏家鈺
開課系所︰機械系
考試時間︰2006-06-27
是否需發放獎勵金：是！！
（如未明確表示，則不予發放）
試題 :
1. In the formula for particle kinematics,
a = (r''-rθ'^2)e_r + (rθ''+2r'θ')e_θ,
the term 2r'θ' represents a) the Coriolis acceleration b) the
acceleraation component required in the radial direction c) an
acceleration component in the transverse direction to maintain motion.
2. Consider recovering the kinetic energy when vehicle brakes, the
1000 kg vehicle is moving at 10 m/sec when brake to stop within
10 m. What is the work consumed by braking a) 0 b) 50 c) 25
Kjoule.
3. The line of imact is a) the line pointion from the contact point
toward the mass center of the second action body. b) the line through
the two mass centers. c) the common normal to the surface of contact.
4. Consider the formula for the angular momentum for a system of paarticles,
H_p = Σ(r_i/p × (m_i)(v_i)), where v_i is the velocity of particle i.
What is the condition on the point P:
a) P is a fixed reference point. b) P must have constant velocity.
c) P has to be the mass center of the system of particles
d) none of the above.
5. Consider the four point masses m connected by rigid massless bars of length
l as shown in the right. What is the resultion acceleration when the
force F is applied?
a) F/4m b) F/2m c) F/2m + (l/2)×(F/2m).
6. In problem 5, what is the resultant angular acceleration α?
a) F/2ml b) F/4ml c) Fl/4m.
7. Consider the bug A on the record is sitting at a distance of r from the
center along the x-axis at this instance as shown in the right. The
record is spinning at a rate of ω. There is a pillar at a distance of
R outside the record. The pillar will appear to have the velocity of
a) rω on the direction of y-axis b) 2(R-r)ω on the direction of y-axis
c) (2r-R)ω on the direction of y-axis. d) none of the above.
8. Consider G is the mass center, ω is the angular velocity of the rigid
body. For an arbitrary point P, which of the following statements is true:
a) H_p = H_G + r_G/P×m(v_G)
b) H_p = r_G/P×m(v_P) + ∫r_/G×(ω×r_/G)dm.
c) H_p = r_G/P×m(v_P) + ∫r_/P×(ω×r_/P)dm.
9. Following the previous question, which of the following statements is true:
a) H_p = r_G/P×m(v_P) - (I^p_xz)ωi - (I^p_yz)ωj + (I^p_zz)ωk
for an arbitrary point P.
b) H_p = r_G/P×m(v_P) - (I^p_xz)ωi - (I^p_yz)ωj + (I^p_zz)ωk
for P located at the mass center.
c) H_p = r_G/P×m(v_P) - (I^p_xz)ωi - (I^p_yz)ωj + (I^p_zz)ωk
for P on the same rigid body of interest.
10.Under what condition does relation
ΣM_p = r_C/P×ma_p + (I^p_z)αk become invalid?
a) P is the mass center, b) P is an arbitrary point.
c) P is an arbitrary point on the body.
d) none of the above.
11.(20%) Consider the 10 kg case slides along the conveyer belt as shown in
the right. At the end it is suppose to tip over at the stop.
Calculate the minimum speed υ at which the case can tip over.
(Assume the case is uniform. The moment of inertia about the axis
protruding the paper is I = (1/12)m(h^2+l^2), where h = 1.0m and
l = 1.5m)
12.(20%) Consider the truck is acceleration along the x-axis at an acceleration
of 10 m/sec^2. A uniform circular cylinder of length 2 m and mass
10 kg is lning against the front end of the truck. The static friction
coefficient between the cylinder and the truck platform is μ. What
is the minimum for μ that the pillar will tip and not slide?
(Note: the moment of inertia of a slander rod with respect to an
axis through its mas center is I = (1/2)ml^2.)
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