Vernier Centripetal Force Apparatus User Manual

Centripetal Force
Apparatus

(Order Code CFA)

The Centripetal Force Apparatus (CFA) facilitates
the study of circular motion. It allows students to
easily and accurately see the relationship between
centripetal force, tangential velocity (or angular
velocity), radius and mass. The traditional method, i.e., twirling a rubber stopper in a
horizontal circle, is instructional in that students can have kinesthetic understanding
of the relationships. For example, they can feel the change in the force as the radius
changes. The CFA allows students to make direct measurements of the variables and
to obtain excellent quantitative data.

With this equipment, students are able to investigate relationships between

 Centripetal force and the mass of the accelerating object
 Centripetal force and the radius of the motion
 Centripetal force and the tangential velocity of the accelerating object
 Centripetal force and the angular velocity of the accelerating object
 Angular acceleration, torque and moment of inertia

What is included with the Centripetal Force Apparatus?

 Rectangular Frame
 Support Legs (2)
 Rotating Assembly consisting of Rotational Shaft, Encoder Wheel, 3-Step Pulley,

Rotating Beam, Bearing Housing

 Sliding Carriage to hold the test masses
 Counterbalance Carriage to balance the rotating beam
 Swivel Assembly (connects Sliding Carriage to a Dual-Range Force Sensor)
 Ultra Pulley
 Ultra Pulley Bracket (preinstalled on Assembly)
 Photogate Bracket with 1/4 x 20 mounting screw (preinstalled on Assembly)
 Dual-Range Force Sensor Bracket (preinstalled on Assembly)
 50 g masses (4)
 100 g masses (4)
 Hook (attaches a Wireless Dynamic Sensor System (WDSS) to the Sliding

Carriage)

 WDSS Mounting Screw and T Nut to secure a WDSS

A Closer Look at the Components

Rectangular Frame

The frame supports the Rotating Assembly and it accommodates a variety of
sensors. Two Pulley Guides on the top of the frame allow a Dual-Range Force
Sensor to be connected to a carriage that slides along the Rotating Beam.

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Rotating Assembly

The Rotating Assembly consists of a Rotating Beam, Rotational Shaft, Bearing
Housing, Encoder Wheel, and 3-Step Pulley. Carriages are placed on the Rotating
Beam. A string can be attached to the 3-Step Pulley to apply a torque to the
Rotational Shaft.

In the middle of the Rotating Beam, you’ll find a Pulley Guide. A string from a
Dual-Range Force Sensor threaded through this pulley can be used to attach the
force sensor to the Sliding Carriage.

Carriages

Two carriages ride on the Rotating Beam during data collection. A Sliding Carriage
(shown at left) has low friction bearings that allow it to slide along the beam during
the experiment. The Sliding Carriage
is attached to a force sensor (e.g., a
Dual-Range Force Sensor or Wireless
Dynamic Sensor System). A
Counterbalance Carriage (shown at
right) is secured to the other side of
the beam using screws and T-nuts. As
the beam rotates, the force sensor
measures the centripetal force on the
Sliding Carriage. A separate sensor
(i.e., a Vernier Photogate) measures
the angular position and angular
velocity.

Swivel Assembly

The Swivel Assembly consists of two strings and a swivel. The assembly is used to
connect the Sliding Carriage to a Dual-Range Force Sensor. A small screw on one
end of the assembly connects to the end of the force sensor. The other end of the
Swivel Assembly contains a loop that slides over a hook on the Sliding Carriage.

Swivel Assembly

Dual-Range Force Sensor Bracket

This bracket is attached to the right side
of the frame. Slide the Dual-Range Force
Sensor onto the post and use the plastic
1/4 x 20 screw that ships with the force
sensor to secure the sensor to the bracket.
A screw on the right side of the bracket
allows the bracket to move up and down,
which enables a change in the radius of
motion of the Sliding Carriage when
attached via the Swivel Assembly.

Photogate Bracket

This bracket, located on the bottom of the frame, allows
you to attach a Vernier Photogate to the frame. A
1/4 x 20 screw is stored in the bottom of the bracket.

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Ultra Pulley and Pulley Bracket

The Ultra Pulley and Pulley Bracket allow a torque to be applied to the Rotational
Shaft. Secure the Ultra Pulley to the bracket using the included 1/4 x 20 screw.
Attach one end of a string to the 3-Step Pulley mounted on the Rotational Shaft.
Attach a small mass to the other end of the string. Run the string over the Ultra
Pulley and allow it to fall to apply a torque to the Rotational Shaft.

Ultra Pulley Ultra Pulley Bracket

WDSS Screw and Clip

The WDSS Screw allows you to attach the WDSS to
the rotating beam. The Clip connects the WDSS to the hook
on the Sliding Carriage.

Masses

Four 50 g masses and four 100 g masses are included in
the apparatus. They slip into the carriages to allow you
to vary the masses of the carriages.

Assembly and Storage of the Frame and Support Legs

The apparatus is shipped flat, and it can be stored flat when not in use. The Rotating
Assembly and Rectangular Frame come completely assembled. The brackets for the
Dual-Range Force Sensor, Vernier Photogate, and Vernier Ultra Pulley are also
preinstalled. The Support Legs are stored on the sides of the frame. Remove the
knob of the knob screw that holds each leg and use the knob screw to attach each
Support Leg to the bottom of the frame, then replace the knob and tighten. Reverse
this procedure to store the equipment.

Rectangular Frame stored flat. Support legs attached to

the underside of the side vertical frame members.

Leveling the Apparatus

Follow these steps to level the apparatus.

1. Secure the Counterbalance Carriage to the outer end of the Rotating Beam.

2. Place three of the Masses in the carriage.

3. Use a flathead screw driver to lower each foot on the CFA footer to its lowest
height.

4. Give the Rotating Beam a very slow spin and watch its motion. The beam will
tend to settle to its lowest point. Confirm the location of lowest point by spinning
the beam a couple more times.

5. Raise the lowest end or side of the apparatus by increasing the height of the
nearby footer or footers.

6. Repeat Steps 4 and 5 until the beam spins without returning to a consistently low
spot.

Attaching the Carriages to the Rotating Beam

It is important to attach the carriages in the proper orientation on the Rotating Beam.
The beam is not symmetric about the Pulley Guide located near the middle of the
beam. With the ruled side of the rotating beam facing you, the Sliding Carriage goes
on the right and the Counterbalance Carriage goes on the left.

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