Download Ch. 9A AP Set

CHAPTER 9 AP SET
For Questions 1 and 2:
Two small balls of clay move over a horizontal frictionless
surface, collide, stick together, and continue moving. Their initial
directions are shown in the diagram to the right. The particles collide
at the origin O. The mass of Ball A is 3m and its speed is V. The mass
of Ball B is 2m and its speed is 2V.

A
B
1) After the collision, the balls move along the dashed line at an angle  with the x-axis. The value of
tangent  is
a) 2/3
b) 3/4
c) 4/3
d) 2
e) 8/3
2) After the collision, A and B move together as a unit at a speed of
a) (1/5) V
b) V
d) (5)1/2 V
c) (7/5) V
e) (3) V
3) A particle of mass m and speed v, collides at right angles with a very massive wall in a perfectly elastic
collision. The magnitude of the change of momentum of the particle is
a) zero
b) (mv)/2
c) 2 mv
d) (2)1/2 mv
e) mv
4) The momentum of a particle in kg m / sec depends on time according to the equation P = 2t2 + 4,
where t is in seconds. At the end of 1 second, the force on the particle in newtons is
a) 2
b) 4
c) 4.7
d) 6
e) 8
5) An unstable nucleus has mass M and is initially at rest. It ejects a particle of mass m with a speed v 0.
The remaining nucleus recoils in the opposite direction with speed
a) v0
b) (m/M) v0
c)
(m/M+m) v0
d) (m+M/m) v0
e) [m/(M-m)]v0
6) A cart of mass 2m has a velocity v0 before it strikes another cart of mass 3m at rest. The two carts
couple and move off together with a velocity
a) (1/5) v0
b) (2/5) v0
c) (3/5) v0
d) (2/5)1/2 v0
For Questions 7 and 8:
A system consists of two objects having mass m1 and m2 (m1  m2).
The objects are connected by a massless string, hung over a pulley as
Shown right, and then released.
e) (2/3) v0

M2
M1
7) When the speed of each object is v, the magnitude of the total linear momentum of the system is
a) (m1 + m2) v
b) (m2 - m1) v
c) (m1 + m2 /2) v
d) (m2 - m1 /2) v2
e) m2v
8) When the object of mass m2 has descended a distance h, the potential energy of the system has
decreased by
a) (m2 - m1) gh
b) m2gh
c) (m1 + m2) gh
d) 1/2 (m1 + m2) gh
e) 0
m0
9) Two particles of equal mass m0, moving with
Equal speed v0 along paths inclined at 600 to the
x-axis as shown at the right, collide and stick together.
Their velocity after the collision has magnitude
a) v0/4
4 kg
6 m/sec
v0
600
m0
c) v0 (2)1/2 / 2
b) v0/2
For Questions 11 and 12:
600
v0
d) v0 (3)1/2 / 2
4 kg
e) v0
4 kg
A 4-kilogram mass has a speed of 6 meters per second on a horizontal frictionless surface, as shown above.
The mass collides head-on and elastically with an identical 4-kilogram mass initially at rest. The second 4kilogram mass then collides head-on and sticks to a third 4-kilogram mass initially at rest.
11) The final speed of the first 4-kilogram mass is
a) 0 m/s
b) 2 m/s
c) 3 m/s
d) 4 m/s
e) 6 m/s
12) The final speed of the two 4-kilogram masses that stick together is
a) 0 m/s
b) 2 m/s
c) 3 m/s
d) 4 m/s
e) 6 m/s
X
X
10 m/sec
6 m/sec
530
Y
15)
Figure I
Figure II
Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 meters per second,
as shown in Figure I above. It then collides elastically with identical ball Y, which is initially at rest. After
the collision, ball X moves at 6 meters per second along a path at 53 0 to its original direction, as shown in
Figure II above. Which of the following diagrams best represents the motion of ball Y after the collision?
a)
b)
v=0
c)
370
10 m/sec
4 m/s
d)
370
8 m/s
e)
530
8 m/s
16) An object of mass m is moving with speed v0 to
the right on a horizontal frictionless surface, as shown
right, when it explodes into two pieces. Subsequently,
one piece of mass (2/5)m moves with a speed (1/2)v0 to
the left. The speed of the other piece of the object is
a) v0/2
b) v0/3
c) 7v0/5
m
d) 3v0/2
v0
e) 2v0
17) A small block of mass 2m initially rests on a track at the bottom of the circular, vertical loop-the-loop
shown above, which has a radius r. The surface contact between the block and the loop is frictionless. A
bullet of mass m strikes the block horizontally with initial speed v0 and remains embedded in the block as
the block and bullet circle the loop. Determine each of the following in terms of m, v0, r, and g.
a)
The speed of the block and bullet immediately after impact.
b) The kinetic energy of the block and bullet when they reach point P on the loop.
c)
The minimum initial speed vmin of the bullet if the block and bullet are to successfully execute
a complete circuit of the loop.
21) A 5-kilogram ball initially rests at
the edge of a 2-meter long, 1.2 -meter
high frictionless table, as shown right.
A hard plastic cube of mass 0.5 kg
Slides across the table at a speed of
26 meters per second and strikes the
ball, causing the ball to leave the table
in the direction in which the cube was
moving. The figure below shows a
graph of the force exerted on the ball
by the cube as a function of time.
a)
Determine the total impulse given to the ball.
b) Determine the horizontal velocity of the ball immediately after the collision.
c)
Determine the following for the cube immediately after the collision.
i)
Its speed
ii)
Its direction of travel (right or left), if moving
d) Determine the kinetic energy dissipated in the collision.
e)
Determine the distance between the two points of impact of the objects with the floor.
22) An open-top railroad car (initially empty and of mass M 0)
rolls with negligible friction along a straight horizontal track
and passes under the spout of a sand conveyor. When the car is
under the conveyor, sand is dispensed from the conveyor in
a narrow stream at a steady rate M / t = C and falls vertically
from an average height h above the floor of the railroad car.
The car has initial speed v0 and sand is filling it from time
t = 0 to t = T. Express your answers to the following in terms
Of the given quantities and g.
a)
Determine the mass M of the car plus the sand that it catches as a function of time t for 0tT.
b) Determine the speed v of the car as a function of time t for 0tT.
c)
i)
Determine the initial kinetic energy K i of the empty car.
ii)
Determine the final kinetic energy Kf of the car and its load.
iii)
Is kinetic energy conserved? Explain why or why not.
d) Determine expressions for the normal force exerted on the car by the tracks at the following
times.
i)
Before t = 0
ii)
For 0tT
iii)
After t = T
23) A motion sensor and a force sensor record the motion of a cart along a track, as shown above. The cart
is given a push so that it moves toward the force sensor and then collides with it. The two sensors record
the values shown in the following graphs.
a)
Determine the cart's average acceleration between t = 0.33 seconds and t = 0.37 seconds.
b) Determine the magnitude of the change in the cart's momentum during the collision.
c)
Determine the mass of the cart.
d) Determine the energy lost in the collision between the force sensor and the cart.
24) A crash test car of mass 1,000 kilograms moving at constant speed of 12 m/sec collides completely
inelastically with an object of mass M at time t = 0. The object was initially at rest. The speed V in m/sec of
the car-object system after the collision is given as a function of time t in seconds by the expression
V = 8 / ( 1 + 5t )
a)
Calculate the mass M of the object.
b) Assuming an initial position of x = 0, determine an expression for the position of the carobject system after the collision as a function of time t.
c)
Determine an expression for the resisting force on the car-object system after the collision as a
function of time t.
d) Determine the impulse delivered to the car-object system from t = 0 to t = 2.0 seconds.