Download Linear Momentum Test Mr. Kepple

Mr. Kepple
Name: _________________________
Linear Momentum Test
Multiple Choice Questions
1
The law of conservation of momentum applies
to a system of colliding objects only if:
5
(A) there is no change in kinetic energy of
the system
A particle moves along the axis. Its
momentum is graphed below as a function of
time. Rank the numbered regions according to
the magnitude of the force acting on the
particle, least to greatest.
(B) the coefficient of restitution is one
(C) the coefficient of restitution is zero
(D) the net external impulse is zero Momentum is
conserved only
when there are
A ball on a rope swings around a pole.
no external
forces acting on
the system.
(E) the collisions are all elastic
2
(A)
(B)
(C)
(D)
(E)
In which direction will the ball fly if released at
the location shown?
(A)
(B)
(C)
(D)
(E)
3
A
B
C
D
E
6
When released the object will
follow a straight line path in the
direction is was initially moving
(tangent to the circle).
1, 2, 3, 4
2, 3, 4, 1
1, 4, 3, 2
1, 3, 4, 2
2, 4, 3, 1
From Newton’s 2nd Law,
the force acting on the
particle is the slope of the
momentum vs. time graph.
A force acting on an object varies as a function
of time according to the equation
,
where is a constant. If the object had an
initial momentum of 0 at time
, what is
the momentum of the object at time ?
(A)
(B)
Circular freeway entrance and exit ramps are
commonly banked to handle a car moving at
13 m/s. To design a similar ramp for 26 m/s
one should:
Impulse is the integral of
force as a function of time.
(C)
∫
(D)
(A) increase radius by factor of 2
(B) decrease radius by factor of 2
(E)
(C) increase radius by factor of 4
(D) decrease radius by factor of 4
( )
7
(E) increase radius by factor of √
4
The momentum of an object at a given instant
is independent of its:
(A)
(B)
(C)
(D)
(E)
At a given instant, the velocity
inertia
mass
would be effectively constant,
speed
therefore momentum does not
velocity
depend on acceleration.
acceleration
In collisions between two objects, kinetic
energy is conserved only
(A) if one of the objects was initially at
rest.
(B) if the two objects have the same mass.
(C) if potential energy converts to work
energy.
(D) in inelastic collisions.
(E) in elastic collisions.
This is just the
definition of an
elastic collision.
8
11
A disk travels along the essentially frictionless
surface of an air hockey table and strikes a
second disk of identical mass that was initially
at rest. Which of the following diagrams shows
the motion of the two disks immediately after
the glancing elastic collision occurs?
A large cannon is mounted on a cart with
frictionless wheels that is initially at rest on a
horizontal surface. The cannon fires a large
cannonball to the right with a speed , which
is then caught by a trap firmly attached to the
cart. What is the final speed of the cannoncart-cannonball system?
(A)
(B)
(C) 0
(D)
(E)
(A)
Since the cannonball is
, to the right caught by the trap, it never
leaves the system. As a
result the momentum, and
, to the left
therefore the speed, will
, to the right
remain zero.
, to the left
One end of a 1 m long string is fixed; the other
end is attached to a 2 kg stone. The stone
swings in a vertical circle, passing the top point
at 4 m/s. The tension force of the string at this
point is about:
9
(B)
(C)
(A) 0
(B) 12 N
(C) 30 N
( )( )( )
( )(
)
(D) 32 N
(E) 52 N
10
(D)
If the total momentum of a system is
changing:
(A) particles of the system must be
exerting forces on each other
(B) the system must be under the
influence of gravity
For a glancing elastic collision of
two objects of equal mass they
must rebound at 90 degrees.
(C) the center of mass must have constant
velocity
(D) a net external force must be acting on
the system
(E) none of the above
The momentum of an object is constant unless a net
force is exerted on it. Since forces internal to the system
cancel out, the only way to change the momentum of a
system is by exerting a net external force.
(E)
12
The difference between a conservative system
and a nonconservative system is
15
(A) Momentum is not conserved in This is just the
definition of a
nonconservative systems.
conservative
system.
(B) Energy is not conserved in
nonconservative systems.
(C) Mechanical energy is not conserved in
nonconservative systems.
(D) In a conservative system mechanical
energy is transformed into thermal
energy.
(A)
(E) In a nonconservative system there is
no change in mechanical energy.
13
A cannon is mounted on a cart, and carrying a
cannonball. The total mass of the cart, cannon,
and ball is , and the car is rolling with no
friction at a velocity in the positive direction as shown above. The ball, of mass
, is fired with a velocity of in the positive
-direction. What is the velocity of the cart
and cannon after the ball is fired?
A 5-kg object can move along the axis. It is
subjected to a force ⃑ in the positive
direction; a graph of ⃑ as a function of time
is shown below. Over the time the force is
applied what is the object’s change in speed?
(B)
Conservation of momentum
Equation:
(
(C)
)
Now solve for
(D)
(E)
16
(A) 0.8m/s
∫
Mud moves
in a circle,
(B) horizontally to the north.
acceleration
(C) horizontally to the south. must be
(D) zero.
centripetal.
(A) vertically upward.
(B) 1.1m/s
(C) 1.6m/s
(D) 2.3m/s
(E) 4.0m/s
14
( )( )
( )
An object moving on a circular path of radius
meters at a constant speed of 4 m/s. The time
required for one revolution is:
(A)
s
(B)
s
(C)
s
(D)
(E) 2/ s
( )
s
A car travels north at constant velocity. It goes
over a piece of mud, which sticks to the tire.
The initial acceleration of the mud, as it leaves
the ground, is…
(E) upward and forward at 45° to the
horizontal.
17
Two bodies of unequal mass, placed at rest on
a frictionless surface, are acted on by equal
horizontal forces for equal times. Just after
these forces are removed, the body of greater
mass will have the…
(A) greater speed
From
, we
(B) greater acceleration see the change in
(C) smaller momentum momentum will be
(D) greater momentum the same for both.
(E) same momentum as the other body
18
Force:
20
(A) equals the negative integral (with
respect to distance) of the potential
energy function
Definition of
(B) is the ability to do work
momentum
(C) is the rate of change of doing work
from
nd
(D) equals the time rate of change of Newton’s 2
momentum
Law:
(E) has dimensions of momentum
multiplied by time
19
(
(
)( )
Two ice skaters, of mass 30 kg and 80 kg, are
skating across the surface of a frozen lake on a
collision course, with respective velocities of
2.0 m/s in a general north direction, and 1.0
m/s generally west, as shown above. After
they collide, the pair of skaters move off in a
direction north of west with a momentum of
approximately 100 kgm/s. How much kinetic
energy was lost in the collision?
A billiard ball hits the side of a pool table at an
angle as shown in the top view above, and
bounces away at the same angle, and with the
same speed. Which vector indicates the
direction of the net change in momentum of
the billiard ball?
(A)
(B)
(C)
(D)
)( )
(E)
⃑
⃑
Vector subtraction, we are looking
for the direction of ⃑
⃑
⃑.
(A) 0 J
𝑣⃑𝑖
(B) 110 J
𝑣⃑𝑓
(C) 55 J
(D) 70 J
( )
𝑣⃑𝑓
(E) 120 J
(
)
From this we see that is a
little less than 50 J.
Since the initial kinetic energy was 100 J
and less than 50 J remains after the
collision, by process of elimination we
choose the answer that 55 J were lost.
𝑣⃑𝑖
Name: ___________________________
Mr. Kepple
Linear Momentum Test
Free Response Questions
Directions: Answer both questions. The suggested time is about 15 minutes for answering each of the
questions, which are worth 15 points each. The parts within a question may not have equal weight.
Show all your work in the spaces provided after each part.
𝑙
𝑚 A
m
A B
B
𝑚
Mech. 1.
Two pendulums A and B are aligned side-by-side such that the bobs of each pendulum just barely
touch. The mass of each string is negligible and has identical length . Pendulum A has mass while
pendulum B has mass
. Pendulum A is pulled back away from the equilibrium position to a height
0.10 meters and then released.
(a) Assuming the system is conservative; calculate the speed of the pendulum A just before it collides
with pendulum B.
√ (
)(
)
√
(b) The collision between the two pendulums is a perfectly elastic head-on collision. Use conservation
principles to write the following equations in terms of ,
, and
.
i. Conservation of momentum
ii. Conservation of kinetic energy. (Use the easy
one if you can remember it!)
(c) Using the equations you wrote down in part (b), calculate the speed of each pendulum immediately
after the collision.
i. speed of pendulum A
ii. speed of pendulum B
(
)
(
(
(
)
)
)
(d) Assuming a conservative system, calculate the maximum height reached by pendulum B.
(
(
)
)
(e) If the two pendulum had the same mass, indicate whether the height reached by pendulum B
would be greater than, less than, or equal to the height you calculated in part (d).
___
X Greater Than
___ Less Than
___ Equal to
Justify your answer.
If the two pendulums had the same mass then the speed of pendulum B after the
collision would be equal to the speed of pendulum A before the collision. As a result
pendulum B would have more kinetic energy after the collision and would therefore
reach a greater final height.
Mech. 2.
A 2-kilogram block and an 8-kilogram block are both attached to an ideal spring (for which
N/m) and both are initially at rest on a horizontal frictionless surface, as shown in the diagram above.
In an experiment, a 100-gram (0.1 kg) ball of clay is thrown at the 2-kilogram block. The clay is moving
horizontally with speed when it hits and sticks to the block. The 8-kilogram block is held still by a
removable stop. As a result, the spring compresses a maximum distance of 0.4 meters.
(a) Calculate the energy stored in the spring at maximum compression.
(
)(
)
(b) Calculate the speed of the clay ball and 2-kilogram block immediately after the clay sticks to the
block but before the spring compresses significantly.
√
√
( )
( )
(c) Calculate the initial speed
of the clay.
)(
(
(
(
)
)
)
In a second experiment, an identical ball of clay is thrown at another identical 2-kilogram block, but
this time the stop is removed so that the 8-kilogram block is free to move.
(d) Indicate whether the maximum compression of the spring will be greater than, equal to, or less
than 0.4 meter.
___ Greater Than
___
X Less Than
___ Equal to
Justify your answer.
With the stopper in place the block and clay came to rest. As a result all of the kinetic
energy of the block and clay was transformed into the elastic potential energy of the
spring. With the stopper removed the blocks are not brought to rest. As a result, a
smaller amount of kinetic energy is transferred to the spring. Therefore the spring
does not compress as great a distance as before.
(e) State the principle or principles that can be used to calculate the velocity of the 8-kilogram block at
the instant that the spring regains its original length. Write the appropriate equation(s) and show the
numerical substitutions, but do not solve for the velocity.
Conservation of Momentum
(
)(
)
Conservation of Energy
(
)(
)