課程名稱︰普通物理學甲上
課程性質︰系內必帶
課程教師︰王立民
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰99/01/14
考試時限（分鐘）：110min
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
普通物理期末考(CH10,11,12,14,15)
試題附圖：http://i814.photobucket.com/albums/zz65/kenyang0531/Untitled-4.jpg
1.In Figure 1,a ladder of length L = 5 m and mass m = 5 kg leans against a
slick (frictionless) wall. The laddar's lower end rests on the pavement with
a maximum coefficient of static friction 0.25 between the ladder and the
pavement. The laddar's center of mass is L/2 form tje lower end. (a) What is
the minimum angle α (in degree) for the ladder which can keep in equilibrium
? (Note that in this case, there is no climber considered.)(10%) (b)
Fallowing the situation in (a), i.e., the angle α is fixed, then a
firefighter of mass M = 50 kg climbs the ladder. What is the vertical height
he can climb?(10%)
2.Figure 2 is an overhead view of a rigid rod that turns about a vertical axle
until the rubber stoppers A and B are forced against rigid walls at distance
rA = 7.0 cm and rB = 4.0 cm from the axle. Initially the stoppers touch the
walls without being compressed. Then force of F magnitude 260 N is applied
perpendicular to the rod at a distance R = 5.0 cm form the axle. (a) If the
two rubber stoppers are identical, what are the magnitudes of the force
compressing stopper A and stopper B?(5%) (b) If the two rubber stoppers are
not identical, both the lengths are 0.5 cm but the corss-sectional area of
stopper A and stopper B are 2.0 and 1.0 cm^2, respectively, what are the
magnitudes of force compressing stopper A and Stopper B?(10%)
[Hint:Using the Young's modulus equation:F/A=E·ΔL/L]
3.An open water tank (Figure 3) contains a hole with a distance h below the
water surface. Here the cross-sectional areas of the tank and the hole are A
and a (A>a), respectively. (a) What is the speed v of the water exiting the
tank?(5% (Denote it with considering the cross-sectional areas of A and a)
(b) What water volume exits the hole in a time interval ΔT?(5%)
4.Using the result:I = M(a^2+b^2)/12 for a slab as shown in Fig. 4(a) and the
parallel-axis theorem, find the inertia of a cube about perpendicular axis
through one edge, where the cube has mass M and edge length of d as shown in
Fig. 4(b).(10%)
5.As shown in Fig. 4(b), this cube slides on a frictionless table plane with a
velocity v, hitting a small ridge (小的狹長隆起物) located at the table edge,
and then rotates. (a) Find the initial magnitude of angular velocity after
the collision.(Use the result in Problem 4).(10%) (b) Find the minimum
velocity v0 for the cube that it can leave this table plane.(15%)(Note that
this is an inelastic collision)
6.If the cube in Fig.5 hass mass 3.0 kg and edge lengths d = 6.00 cm, and is
mounted on an axle through its one edge at bottom. A spring (k = 1200 N/m)
connects the cube's upper corner to a rogod wall. Initially the spring is at
its rest length. If the cube is rotate 3° and released, (a) what is the
period of the resulting SHM?(10%) (b) What is the maximum magnitude of
angular velocity during the SHM?(10%)
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