Download Lab 35 Linear Impulse and Momentum

LAB #35 IMPULSE AND MOMENTUM.
Lab 35 Setup – Figure 1
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LAB #35 IMPULSE AND MOMENTUM.
OVERVIEW
A body in motion has linear momentum. Linear momentum is defined as the product of the mass
and velocity of an object.
𝒑 = 𝑚•𝒗
In the SI system:
m is the mass in kg
v is the velocity in m/s
p units are kg • m/s
Since velocity is a vector quantity (having both magnitude and direction), linear momentum is
also a vector quantity. Its direction is the same as the object's direction of motion.
Impulse is defined as the product of force and the time interval for which the force acts on the
object.
𝐼𝑚𝑝𝑢𝑙𝑠𝑒 = 𝐹 • 𝛥𝑡
If a system is isolated (no outside force acts on it), then linear momentum is conserved. But if an
external force acts on the system, its linear momentum will change. The change in momentum of
the system will be equal to the impulse.
𝐼𝑚𝑝𝑢𝑙𝑠𝑒 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝐹𝛥𝑡 = 𝑚𝑣 = 𝛥𝑝
If a change in momentum occurs in a short period of time, the force required may be large. That
is why, when catching a ball, a catcher moves his hand in the direction of motion of the ball. By
doing this, he prolongs the time of impact. This reduces the force which the hand must exert to
stop the ball. The same principle is applied to automobile bumpers. When an automobile without
bumpers hits an object, the change in momentum is very rapid. Thus a rather large force acts on
the car, causing considerable damage. On the other hand, with bumpers, the time of impact is
prolonged. The bumper's springs take longer to compress, and the damaging forces are reduced.
In this experiment, a weight will be dropped on a spring, causing it to compress. The applied
impulse depends on the mass of the dropped object and its velocity at impact. The time of
compression depends on the stiffness of the spring. You will observe the effect of spring stiffness
on the average force of impact.
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LAB #35 IMPULSE AND MOMENTUM.
OBJECTIVES: Upon successful .completion of this experiment, you should be able to:
A) Measure the impulse time when an object collides with an obstacle.
B) Determine the compression of a spring and calculate its spring constant.
C) Demonstrate that the impulse of a throe equals the change in momentum.
D) Find the average force on the spring, knowing that the force equals the time rate of change of
momentum.
EQUIPMENT REQUIRED:
Impulse Measurement Equipment
Two Springs of Different Stiffness
AC/DC Power Supply
Triple Beam Balance
Universal Lead Set
Perforated Metal Cylinder
PROCEDURE:
The setup used in this experiment is shown in Figure 1. Refer to this figure and the detailed
figures that follow when assembling your equipment.
A) 1. Using the electrical leads, connect the impulse measurement equipment to the timer (there
are three leads). Observe proper polarity. Set the timer to read impulse time by selecting impulse
measurement on the mode selector switch. See Figure 2.
2. Slide the spring platform down over the
upright rod on the impulse measurement
equipment. Select the less stiff spring for the
first trial. Place the spring over the rod on top
of the spring platform as shown in Figure 2.
3. Put the second cylinder on the spring with
its open end towards the bottom as shown in
Figure 2.
4. Adjust the power supply voltage4 to
minimum and turn it on.
5. Slowly adjust the power supply to 10 V DC.
Set the impulse measurement equipment to
zero by depressing the switch once.
6. Measure the mass of the cylinder, and
record in Data Table 1.
7. Put the perforated cylinder on the upright rod. Do this gently so as not to start the timing
mechanism.
8. Bring the ring on the lower cylinder in contact with the lip of the upper cylinder.
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LAB #35 IMPULSE AND MOMENTUM.
COLLECTING DATA:
B) 1. Read the position of the ring on the scale on the-lower plastic cylinder. (Make sure the ring
is in contact with the lip of the upper plastic cylinder.) See Figure 3. Record this reading as hl in
Data Table 1.
2. Measure the height through which the weight will fall. Measure from the top of the upright
rod to the top of the weight as it sits on the upper cylinder. See Figure 4. Record this distance in
meters as H in Data Table 1.
3. Raise the weight so it is flush with the top of
the rod. Now release the weight. As the spring
is compressed, the upper plastic cylinder
pushes the ring down.
4. Read the position of the ring and the time
reading on the digital clock, but do not yet
record them. For the final reading, the ring
should not interfere with the motion of the
cylinder, but should serve only as a marker.
You will need to make sure that the position of
the ring and time readings are consistent.
5. Lift the weight to the top and reset the timer.
Do not adjust the ring.
6. Repeat steps B-3 through B-5 until the
readings are consistent. Now the position of the ring indicates the amount of compression of the
spring caused by the impact of the falling weight. Find the consistent final position for the ring
and the consistent final reading for the timer. Record these as h2
and h = h2 – h1 in meters in Data Table 1.
7. In a previous lab on energy of a compressed spring, the Hooke's
Law constant was determined by compressing a spring. We will
use a similar procedure to determine the Hooke's Law constant, k,
for these springs.
Remove the weight from the apparatus. Observe the position of the
bottom of the cylinder. Place the weight on the top of the cylinder.
Do this gently so that the bottom of the spring support does not
move. Observe the new location of the cylinder bottom. By
subtraction, determine the length of compression caused by the
weight. Record this as d in meters in the last column of Data Table
1.
8. Repeat steps B-1 through B-7 for the stiffer spring. Record all
data in Data Table 1.
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LAB #35 IMPULSE AND MOMENTUM.
C) CALCULATIONS:
1. Calculate the gravitational potential energy Ep , of the perforated cylinder at height H, using
the equation Ep = m·g·H.
2. The law of conservation of energy states that the kinetic energy of the metal cylinder just
before impact equals the potential energy of the weight at the height from which it was released.
Since friction between the cylinder and the shaft changes some of the potential energy to heat,
we do not know the actual kinetic energy just before impact.` the maximum possible kinetic
energy will be equal to the potential energy. Record the value of E determined above as the
maximum Ek .
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3. The for the kinetic energy of a moving object is 𝐸𝑘 = 2 · 𝑀 · 𝑉 2 . Rewriting the equation as 2 ·
𝐸𝑘
= 𝑉 2 ., solve for the value of 𝑉 2 , and then take the square root to find v. Record this as the
maximum velocity of the perforated cylinder at impact.
𝑀
4. Find the maximum momentum of the metal weight just before impact using the equation 𝑝 =
𝑚 · 𝑣. Record the answer in Table 2.
5. Determine the spring constant, k for each spring by dividing the weight (𝑤 = 𝑚 · 𝑔) by the
distance, each spring was compressed when the weight was at rest on the spring. Use the
equation:
𝑚·𝑔
𝑘 = 𝑑 (units of N/m)
Record the k value in Table 2 for each spring.
6. When the spring is compressed, it exerts an upward force on the metal mass. At the "rest"
position, the upward force cancels the downward pull of gravity. This means that when the timer
starts, the net force is zero. As the spring compresses further, the force causing the impulse
increases from zero to a maximum of 𝐹max = 𝑘 · 𝑑, where 𝑑 = ℎ2 − ℎ1 . Find the approximate
average force for each spring using the formula below. Record the answer in Table 2.
Fav J=0.6(k·d) (approximate)
7. Calculate the impulse, using the equation 𝐼𝑚𝑝𝑢𝑙𝑠𝑒 = 𝛥𝐹𝑎𝑦 • 𝑡
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LAB #35 IMPULSE AND MOMENTUM.
LAB 35: IMPULSE AND MOMENTUM
OBJECTIVES:
DATE___________
SKETCH:
DATA TABLE 1
SPRING
USED
MASS OF
CYLINDER
m
(kg)
HEIGHT
CYLINDER
FALLS
THROUGH
H
(m)
MEASURED
IMPACT TIME
INTERVAL
t
(sec)
INITIAL
POSITION
OF RING
FINAL
POSITION
OF RING
h1 (m)
h2 (m)
IMPACT
DISTANCE
HOOKE'S
LAW
COMPRESSIO
h2 - h1
d (m)
d (m)
LESS
STIFF
MORE
STIFF
DATA TABLE 2
SPRING
USED
MAXIMUM
KINETIC
ENERGY
MAXIMUM
VELOCITY
AT
IMPACT
MAXIMUM
MOMENTUM
OF FALLING
WEIGHT
v (m/s)
p = mv
(kgm/s)
EK (J)
SPRING
CONSTANT
k
(N/m)
AVERAGE
IMPULSE
FORCE
Fav (N)
CALCULATED
IMPULSE
Favt
(Nsec)
LESS
STIFF
MORE
STIFF
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LAB #35 IMPULSE AND MOMENTUM.
LAB 35 ANALYSIS
1. Compare the change in momentum of the metal cylinder (assuming conservation of energy)
with the calculated impulse. Are the values approximately equal? Explain why they were or
were not the same.
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2. A stiffer spring should have a greater impulse force and shorter time of impact. Was this
supported by your data?
___________________________________________________________
3. When a moving object is brought to a full stop, as in a collision, the change in momentum is
pre-determined. How can you reduce the average force of impact in a collision?
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4. When a golfer hits a ball, the average force on the ball is limited by the golfer's strength.
How can a golfer increase the momentum given to the ball?
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Use the 5-step method to solve the following problem.
5. A 20 kg cart is moving along a level road at 4.0 m/s. A constant forward push of 12.0
newtons is applied for 2.5 seconds.
A) What is the original momentum of the cart?
B) What is the magnitude of the applied impulse, in newton-seconds?
C) How much change of momentum occurs, in kgm/s?
D) What is the final momentum of the cart?
E) What is the final velocity of the cart?
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