Download lab 16 centripetal force - acceleration

LAB 16 CENTRIPETAL FORCE AND ACCELERATION
May 7, 2017
OVERVIEW:
A body that is travelling in a circle at constant speed is undergoing uniform circular
motion. In figure 1 v = vector velocity where the direction of the velocity is continually changing
as the body moves around the circle, but the magnitude of the velocity remains constant.
Since the velocity is changing direction there must be an acceleration which requires that
a force act on the body. Since the path that the body is following is a circle, the force acting is
directed toward the center of the circle.
The acceleration on the body is called Centripetal Acceleration and the force acting on
the body is called Centripetal Force. Centripetal Force = the net inward force on a body in a
curved or circular path. If a body is swung at the end of a string and the string breaks, the ball
will travel in a straight line tangent to the circle from the point the ball was located at the time
the string broke.
Planets are kept in their orbits by a gravitational force which provides the centripetal
force required for circular motion. In a similar manner the gravitational force of attraction of the
earth for satellites in orbit about the earth provides the centripetal force to keep the satellites in
orbit. Cars derive their centripetal force for their turns on the highway from the frictional force
between the tires and the pavement and/or the banking angle of the highway.
𝛥𝑣
𝐶𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑎𝑐 =
𝛥𝑡
Δv = 𝑣B - 𝑣A . v is a vector, and v is determined by the change in direction (see figure 1a), even
though the magnitude (speed) may remain constant. Mathematically, the magnitude of the
acceleration is given by the equation 𝑎𝑐 =
2
𝑣2
𝑟
where v is the speed, and r is the radius of the
circular path. The equation 𝑎𝑐 = 𝜔 · 𝑟 may also be used to find the centripetal acceleration.
Newton's second law (𝐹𝑛𝑒𝑡 = 𝑚 • 𝑎) can be applied to the case of uniform circular
motion. The net force causing an object to move in a circle is the centripetal force. By
substituting 𝐹𝐶 , for 𝐹𝑛𝑒𝑡 , and using the formula for acceleration given above, we have
𝐹𝐶 = 𝑚 ·
𝑣2
𝑟
= 𝑚 · 𝜔2 • 𝑟
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LAB 16 CENTRIPETAL FORCE AND ACCELERATION
May 7, 2017
OBJECTIVES:
A. To study centripetal force, orbital velocity and the mass of an object travelling in a
circle at constant speed.
B. To determine the centripetal force by experiment and compare it to the actual
centripetal force.
EQUIPMENT REQUIRED:
Glass tube with a cord threaded through it
Rubber stopper at one end of the cord
Washers to be attached to other end of cord
Paper clips and masking tape
Stopwatch or watch with sweep second hand
PROCEDURE:
A. Preparation:
1. Find the mass of the rubber stopper and record its mass
in the data table.
2. Find the mass of 5 washers and record the mass in the
data table.
3. Practice whirling the rubber stopper maintaining a
velocity so that the marker (masking tape) stays at a
constant distance below the bottom of the glass tube. See
the diagram to the right.
CAUTION: BE CAREFUL SWINGING THE STOPPER SO THAT IT DOESN'T HIT ANYONE
INCLUDING YOURSELF.
B. Experiment:
1. Whirl the stopper in a horizontal plane at a steady speed with 5 washers on the line.
2. With the help of a lab partner, measure the distance of the masking tape below the bottom of
the glass tube while the rubber stopper is spinning at the constant speed.
3. Using a stopwatch measure the time to make 40 revolutions of the rubber stopper and record it
on the data sheet.
4. Find the period, T, of one revolution by dividing the time for 40 revolutions by 40 and record
this time on the data sheet.
5. Place the tube, stopper and cord on a flat surface and measure the radius of the circular orbit,
the distance between the middle of the rubber stopper and the top of the tube, with the masking
tape at its measured location when you were whirling it. Record the radius on the data sheet.
6. Repeat steps A2, and B1-5, above for 10 washers and for 15 washers.
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LAB 16 CENTRIPETAL FORCE AND ACCELERATION
May 7, 2017
7. Replace all of the equipment for this experiment and complete the below calculations and the
lab form.
CALCULATIONS:
1. Calculate the weight of the washers for each of the three runs and enter the results in Data
Table 2. This is the actual Centripetal force for your experiment.
2r
2. Calculate the orbital velocity, v, by the formula: v =
for each of the three runs and record
T
the results in Data Table 2.
NOTE: r must first be converted from centimeters to meters prior to calculating the orbital
velocity.
v2
3. Calculate the experimentally determined value of Centripetal Force Fc = m for each of the
r
three runs and enter these values in Data Table 2.
NOTE: here, m is the mass of the rubber stopper that you measured in step A1 above in
kilograms.
4. Compute the Percentage Difference between the actual (the weight of the washers) and
experimental value of Centripetal Force for each of the three runs and enter the results in Data
Table 2.
% Difference =
|actual value−experimental value|
𝑎𝑐𝑡𝑢𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
x 100%
5. Discuss the questions on the back of the lab form with your partners, and fill in the answers
that you agree upon. If you cannot agree on a specific question, ask for help from the instructor.
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LAB 16 CENTRIPETAL FORCE AND ACCELERATION
LAB 16: CENTRIPETAL ACCELERATION
OBJECTIVES:
May 7, 2017
DATE:_______
SKETCH OF LAB SET-UP:
DATA TABLE 1
Mass of Rubber Stopper: __________ kg
Trial
Mass of
Washers
m (kg)
Tube-toTape
Distance
(cm)
Time
for 40
revs
t (sec)
Period of
one rev
T (sec)
Orbital
Radius
r (cm)
#1
#2
#3
DATA TABLE 2
Trial
Actual
Weight of
Washers
Fc (newtons)
Orbital
Speed
v
(m/s)
Experimental
Centripetal
Force
Fc = mv2/r
(newtons)
Percentage
Difference
in Fc
Values
#1
#2
#3
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LAB 16 CENTRIPETAL FORCE AND ACCELERATION
LAB 16 ANALYSIS
May 7, 2017
CENTRIPETAL ACCELERATION
1. Discuss the possible errors in the experimental values of FC that cause them to be different
from the actual values.
________________________________________________________________
______________________________________________________________________________
2. Show that the expressions mv2/r and mr2 both have the units of force in both English and SI
systems.
USE THE 5-STEP METHOD TO SOLVE THE FOLLOWING PROBLEMS:
3. A 0.5 kg ball moves in a circle 0.4 m in radius at a speed of 4.5 m/s. What is its centripetal
acceleration? What is the centripetal force on the ball?
4. A 4000 lb. car travels at constant speed on a circular track with a 300 ft. radius. The car
completes a single lap in 32 sec. Find the velocity of the car, its centripetal acceleration and the
centripetal force acting on the car. Lastly, describe the source of the centripetal force since no
cord is attached to the car.
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