AAPT Quiz
1996 Physics Olympiad Screening Test (Part 1)
1. An object is projected straight upward from ground level with a velocity of 50 m/s. Ignoring air resistance, it will return to ground level in approximately:
A. 2.5 s
B. 5.0 s
C. 7.5 s
D. 10 s
E. 15 s
2. A jogger runs with constant speed
v
through a forest of pine trees. A pine cone starts to fall from a height
h
when the jogger is directly below it. How far behind the jogger will the pine cone land?
3. A ball is thrown downward with speed 15 m/s from the roof of a 30 m building. At the same instant a ball is thrown upward with speed 15 m/s from ground level. Relative to ground level, the two balls pass each other at a height of:
A. 0
B. 5.0 m
C. 10 m
D. 15 m
E. 20 m
4. A swimmer can swim with a velocity of 1.0 m/s in still water. The swimmer wishes to swim directly across a river with a current of 0.50 m/s directed from upstream to downstream. To end up directly across the river the swimmer must head at an angle of:
A. tan
^{-1}
(½) upstream
B. sin
^{-1}
(½) upstream.
C. directly across the river.
D. sin
^{-1}
(½) downstream
E. tan
^{-1}
(½) downstream
5. What is the tension
T
in the rope if the 10-N weight is moving upward with constant velocity?
A. 3.5 N
B. 5.0 N
C. 7.1 N
D. 10 N
E. 14 N
6. As shown, two blocks with masses
m
and
M
(M > m) are pushed by a force
F
in both Case
I
and Case
II
. The surface is horizontal and frictionless. Let R
_{I}
be the force that
m
exerts on
M
in case
I
and R
_{II}
be the force that
m
exerts on
M
in case
II
.
Which of the following statements is true?
A. R
_{I}
= R
_{II}
= 0
B. R
_{I}
= R
_{II}
and is not equal to zero or F.
C. R
_{I}
= R
_{II}
= F
D. R
_{I}
< R
_{II}
E. R
_{I}
> R
_{II}
7. Two blocks, with masses 17 kg and 15 kg, are connected by a light string that passes over a frictionless pulley of negligible mass as shown. The surfaces of the planes are frictionless. The blocks are released from rest. T
_{1}
and T
_{2}
are the tensions in the strings.
Which of the following statements is correct?
A. The 15-kg block accelerates down the plane.
B. The 17-kg block accelerates down the plane.
C. Both blocks remain at rest.
D. T
_{1}
> T
_{2}
E. T
_{1}
< T
_{2}
8. A small block of mass
m
starts from rest at the top of a globe of radius
R
.
At what angle θ does it slide off the surface of the globe? Assume the system is frictionless.
A. θ = 0º
B. θ = cos
^{-1}
(1/3)
C. θ = cos
^{-1}
(2/3)
D. θ = 60º
E. θ = 90º
9. An object with mass
m
and initial velocity
v
is brought to rest by a constant force
F
acting for a time
t
and through a distance
d
. Possible expressions for the magnitude of the force F are:
mv
^{2}
/2d
2md/t
^{2}
mv/t
Which of these give(s) the correct expression for the magnitude of the force F?
A. ii only
B. iii only
C. i and ii only
D. ii and iii only
E. i, ii, and iii
10. A small sphere is moving at a constant speed in a vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.
kinetic energy
potential energy
momentum
Which of these quantities will change as this sphere moves around the circle?
A. i and ii only
B. i and iii only
C. ii only
D. iii only
E. ii and iii only
11. A roller coaster travels with speed
v
_{A}
at point A. Point B is a height
H
above point A. Assuming no frictional losses and no work done by a motor, what is the speed at point B?
12. Three air track cars are initially placed as shown in the accompanying figure.
Car A has mass
m
and initial velocity
v
to the right.
Car B with mass
m
and car C with mass
4m
are both initially at rest.
Car A collides elastically with car B, which in turn collides elastically with car C. After the collision, car B is at rest.
The final velocities of cars A and C are:
A. Car A: 0.6v to the left
Car C: 0.4v to the right
B. Car A: 2.6v to the left
Car C: 0.4v to the right
C. Car A: at rest
Car C: 0.5v to the right
D. Car A: at rest
Car C: 0.25v to the right
E. Car A: at rest
Car C: v to the right
13. A child with mass
m
is standing at the edge of a playground merry-go-round with moment of inertia
I
, radius
R
, and initial angular velocity
ω
. The child jumps off the edge of the merry-go-round with tangential velocity
v
with respect to the ground.
The new angular velocity of the merry-go-round is:
14. As shown, a spool has outer radius
R
and axle radius
r
. A string is wrapped around the axle of the spool and can be pulled in any of the directions labeled by
I
,
II
, or
III
.
The spool will slide to the right without rolling on the horizontal surface if it is pulled in direction(s):
A.
I
only
B.
II
only
C.
III
only
D.
I
and
II
only
E.
II
and
III
only
15. A uniform flag pole of length
L
and mass
M
is pivoted on the ground with a frictionless hinge. The flag pole makes an angle
θ
with the horizontal. The moment of inertia of the flag pole about one end is
1/3 ML
^{2}
.
If it starts falling from the position shown in the accompanying diagram, the linear acceleration of the free end of the flag pole – labeled P – would be:
PSRC
at
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