課程名稱︰普通物理學甲
課程性質︰必修
課程教師︰李尚凡
開課學院：工學院
開課系所︰機械
考試日期（年月日）︰07/11/09
考試時限（分鐘）：2小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A fireworks rocket explodes at height h , the peak of its vertical
trajectory. It throws out burning fragvments in all directions,but all at the
same speed v.Pellets of solidified metal fall to the ground without air
resistance,Find the smallest angle that the final velocity of an impacting
fragment makes with horizontal.
2 A rocket of mass M moves along an x axis at the constant speed vi=40m/s.
A small explosion seperates the rocket into a rear section of mass m1 and a
front section;both sections move along the x axis.The relative speed between
the rear and the front sections is 20m/s.What are (a)the minimum possible
value of final speed vf of the front section and(b)for what limiting value
of m1 occur?(c) What is the maximum possible value of vf and(d) for what
limiting value of m1 does it occur?
3. A small,spherical bead of mass 3.00 g is released from rest at t=0 in a
bottle of liquid shampoo and experiences a resistive force R=-bv. The terimal
speed is observed to be υ=2.00cm/s . Find(a)the value of the constant b,(b)
the time τ at which it reach 0.632υ,and (c)the value of the resistance force
when the bead reaches the terminal speed.
4. A single conservative force acting on a particle with a potential energy
function U(x)=(1-x)x.x.e︿-x associated with this force (a)Calculate the force
.(b)Find the stanble and unstable equilibrium positions x's.
5. Find the center of a uniform solid cone of height h and semiangle α.
6. In the figure blew, the incline has mass M and is fastened to the station-
ary horizontal tabletop. The block of mass m is placed near the bottom of the
incline and is released with a quick push that sets it sliding upward.It stops
near the top of the incline ,as shown in the figure ,and then slides down again
,always without friction.Find the force vector that the tabletop exerts on the
incline throughout this motion.
7. A 7.00g bullet,when fired from a gun into a 1.00 kg block of wood held in
a vise,penetrates the block to a depth of 8.00cm .This block of wood is next
placed on a frictionless horizontal surface, and a second 7.00g bellet is fired
from the gun into the block. To what depth will the bellet penetrate the block
in this case?
8. A rocket has total mass Mi,inculding fuel and oxidizer.In interstellar
space,it starts from rest at the position x=0,turns on its engine at time
t=0,andputs out exhaust with relative speed ve at the constant rate k.The fuel
will last for an actual burn time less than a defined "projected depletion time"
"as Tp=Mi/k (which would be the burn time if the rocket could use its payload
and fuel tanks ,and even the walls of the combusion chamber as fuel.)Find ,
during the burn ,(a)the position,(b) the velocity,and (c) the acceleration of
the rocket as a function of time.
9. A 1.34kg object is attached to a vertical rod by two massless strings as
shown in the figure. The object rotates in a horizontal circle with bothstrings
tight. The tension in the upper string is 35.0 N.What is the(a)tension in the
lower string,(b) magnitude and direction of the net force F ,and (d) speed of
the ball?
10. a rod at rest in frame S' has a length of L' and makes an angle ofθ' with
respectto the x' axis.Frame S' moves at velocity +v relative to frame S ,as
shownin the figure.(a)What is the length l of the rod in frame S in term of
L' θ',V,and c?(b)What is the oriention angle in Sframe in term of θ'and
β or γ?
(c)(extra points!) If the object is a 3-D cube of length L, an observer in
frame S will see the cube undergoes an apparent rotation. What is the rotation
angle?
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