九十三學年度第一學期普通物理第一次段考
機一甲
93.11.10
1st hoop
2nd hoop
1. As shown in Fig. 1, a ball was shot from a toy gun at a height
h=3.00 m and finally reached a target at the same height.
During the time in the air, the ball passed 2 hoops. The ball
D
passed 1st hoop at 1.00 s and passed 2nd hoop at 5.00 s after
h
shooting. The two hoops are at the same height with
separated distance D=40 m.
Fig. 1
(a) What is the horizontal distance from the shooting point to the target? (4%)
(b) What are the magnitude and the angle relative to ground of the ball’s initial velocity?
target
h
(5%)
(c) What is the height of the hoops? (5%)
m1
2. In Fig. 2, m1 does not move relative to m3, and all the ropes are
massless and taut. Determine the magnitude of the force F exerted
on the large block m3. Assume m2 does not contact m3 and ignore
all friction. (10%)
F
m3
m2
Fig. 2
L
3. A 4.00 kg ball is connected by two massless strings to a rotating
rod. As shown is Fig. 3, the length of the strings L=3.00 m is the
same as the distance between strings’ connections. The rod rotates
horizontally. What is the magnitude of a string’s tension (a) when
the ball is at the lowest position, (5%) and (b) when the ball is at
the same height as the rod? (5%)
L
L
Fig. 3
y
4. As shown in Fig.4, a particle moves along a quadro-circle
trajectory in the horizontal plane. A conservative force (F) field
with direction as shown in Fig. 4 is applied everywhere.
d
C
E
F
45
(a) Find the work done by the centripetal force of the circular motion
when the particle moves from E to A. (5%)
A
x
(b) Find the work done by the conservative force F when the particle
d
moves from E to A. (5%)
Fig. 4
(c) If the particle had speed v0 at pint E, what is its kinetic energy at point A. (5%)
(d) As the condition in (c), if the particle elastically bounced back at point A and moves to
point C, what is its kinetic energy at point C? (5%)
(e) What is the power transferred from the conservative force to kinetic energy at point A
and point E? (6%)
o
5. Particle A (4 kg) and particle B (2 kg) are put on a frictionless surface and connected by
a spring with spring constant 200 N/m. The spring was first compressed 80 cm and then
released freely. What is the kinetic energy of A and B when the spring returns to its
original length? (10%)
6. Consider a cylinder of mass M and radius R rolling down an
incline with a inclining angle  as shown in Fig. 5. The coefficient
of static friction between the cylinder and the incline is . If the
cylinder is in pure rolling motion without slipping,
(a) What is the linear acceleration of the center of mass for the
cylinder? (7%)
R

Fig. 5
(b) What is the minimum value of ? (4%)
(The rotational inertia of a solid cylinder about its central axis is 0.5 MR2)
7. A particle of mass m in Fig. 6 slides down a frictionless surface
from height h and collides with the uniform vertical rod, sticking to
it. The rod has mass M and length L. The rod pivots about O
through maximum angle .
(a) Find the rotational inertia of the rod with respect to the rotation
axis through O (5%).
(b) Find the angular velocity of the vertical rod just after collision.
(7%).
O

L
h
Fig. 6
(c) Find the maximum angle . (7%)
(The rotational inertia of a rod about axis through center of mass and perpendicular to length
is
1
ML2.)
12
m