Experiment 7: Centripetal Force
Figure 7.1
EQUIPMENT
Two-Meter Stick
Pendulum Clamp and Rod
Table Clamp
String
Mass Hanger
Masses: (3) 100g, (1) 500g
Lab Pro Interface and Connections
Dual-Range Force Sensor
Motion Detector
Protractor
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Experiment 7: Centripetal Force
40
Advance Reading
Text: Centripetal force, gravitational force.
Objective
To measure the centripetal acceleration of a body in
circular motion and to determine the centripetal force
on the body.
Theory
An object that moves in a circular path undergoes centripetal motion (Greek: “center seeking”). Such an
object has a changing velocity, since its direction of
motion changes constantly as it moves around the circle. Thus, the object undergoes centripetal acceleration, ac , related to its speed (v) and the size of the
circle (radius, r):
v2
ac =
(7.1)
r
A force must be applied to an object in order to cause it
to experience centripetal acceleration and move around
the circular path. The required force can be determined by applying Newton’s Second Law:
Fc = mac = m
v2
r
(7.2)
Though an object may be subjected to multiple forces,
the net force it experiences will always be equal to
mv 2 /r if it moves in a circular path.
Figure 7.2: Simple Pendulum
A simple pendulum exhibits centripetal motion, as it
swings in a circular path. At the bottom of its swing,
all forces act on the pendulum in the vertical direction. In this case, the net force Fc will be equal to the
vector sum of the tension holding up the pendulum’s
suspended mass and the force of gravity pulling the
mass downward.
At the bottom of the swing, the pendulum’s velocity
and supporting tension force are maximized. As the
pendulum swings out to either side, its velocity becomes zero, as does its centripetal acceleration. Tension force reaches a minimum in this position.
This scenario will be examined hanging a pendulum
from a force probe and swinging it through the path
of a motion detector. Capturing the motion of the
pendulum with the motion detector can require fine
coordination. Rest the detector on the floor and hang
the pendulum as close to the floor as possible.
Be sure that the pendulum’s direction of motion is
aligned closely with the axis of the detector, that the
pendulum does not leave the detector’s cone of measurement, and that it does not approach the detector
closer than approximately 0.5 meters.
Prelab 7: Centripetal Force
41
Name:
1. What are centripetal acceleration and centripetal force? Give equations and a brief explanation. (20 pts)
2. Draw a force diagram (e.g., Fig. 5.3) of a simple pendulum at the bottom of its swing. (20 pts)
3. Using your force diagram, write an equation relating the centripetal force (net force) to all other forces acting on
the pendulum. (20 pts)
4. A wrecking ball (800 kg) swings from a crane in a circular path of radius 20 m. At the bottom of its swing, it
moves with a speed of 10 m/s; calculate the centripetal force that acts on the ball. (20 pts)
5. How much tension does the support cable need to withstand to support the wrecking ball in Prelab Question 4?
(20 pts)
Experiment 7: Centripetal Force
42
PROCEDURE
1. Open Logger Pro and connect the force sensor and
motion detector to the lab pro.
2. Calibrate the force sensor (Experiment ) Calibrate
) Lab Pro) by hanging two known weight from the
sensor and inputting the corresponding force (one
can be zero newtons).
PART 1: Measuring Centripetal Force
3. Suspend 0.550 kg from the force probe with a length
of string between 1.0 and 1.5 meters long. Measure the distance “r” from the top of the pendulum
(above the force probe) to the center of mass of the
hanging mass.
4. Measure the weight of the hanging mass, Fg , and
record it in the table provided.
5. Move the pendulum 15 from vertical and release it.
Capture its motion with the motion detector while
simultaneously recording tension force.
6. Using the Examine tool (Analyze ) Examine), select a peak on the velocity graph and determine the
maximum velocity of the swing. Record this measured value in the table provided.
7. Calculate the centripetal force associated with a velocity vmax in a circular path. Use this value to determine the theoretical tension in the pendulum at
the bottom of the swing.
8. Examine the corresponding peak on the force graph.
Record the maximum tension force Tmax of the
swing.
9. Repeat Measuring Centripetal Force for hanging
masses of 0.350 kg and 0.250 kg.
10. Set the document to landscape (File ) Page Setup).
Print a copy of all graphs for the final experimental
setup, m = 0.250 kg (File ) Print).
PART 2: Zero Tangential Velocity
11. Using Logger Pro, find the tension force in the pendulum at the highest point in its swing. Compare
this to the part of gravity that acts along the pendulum. Show your work and record this values in
the table provided.
Figure 7.3