Liquid Accelerometer

Introduction

The surface of a liquid often forms a nice visualization of the external forces acting upon the liquid. In this demonstration, a tray of water is spun in a circular fashion to see what happens to the surface of the liquid.

Concepts

• Uniform circular motion
• Centripetal force

Materials

Safety Precautions

Although this demonstration is considered nonhazardous, please follow all normal laboratory safety guidelines.

Disposal

With proper care, the demonstration device can be used indefinitely. The accelerometer should be cleaned and dried prior to storage.

Prelab Preparation

Fill the demonstration apparatus with water to a depth of approximately 2". If desired, add a few drops of food coloring to the water to make the water more visible. Conduct a practice run of the demonstration before class to test for leaks and proper operation.

Procedure

1. Spin the water chamber above the axle of the accelerometer device. Hold your hand on top of the device above the axle and spin the device with a smooth, twisting motion. With practice you will be able to spin the device in an even and continuous fashion (see Figure 1).
   {13919_Procedure_Figure_1_Spin entire device with hand over the top of the apparatus}
2. When the accelerometer is spun in an even fashion, a characteristic parabolic shape is observed on the upper surface of the water.
3. (Optional) Add a floating ball to the water in the accelerometer. Place it on the outside. When the accelerometer is spun, watch as the floating ball “moves toward the center of the accelerometer,” creating a centripetal motion paradox.

Teacher Tips

• This device is durable and can be used for many years. The plastic chamber should be handled with care. The axle can be waxed or lubricated periodically if it does not spin freely.
• The axle can be removed from the base and placed in a rotator to demonstrate what happens with continuous and constant rotary motion.
• (Optional) The floating ball will “fall” until the centripetal acceleration is balanced by gravitational acceleration on the curve of the parabola.

Discussion

Uniform circular motion results when the net force acting upon a mass moving at a constant speed changes direction in such a way that the mass is deflected into a circular path. The force is always acting at a right angle to the direction that the mass is moving. The force causing this reaction is called the centripetal force.

Note that the centripetal force always acts at right angles to the instantaneous velocity of the mass. Therefore, the centripetal force does not change the magnitude of the velocity. Since velocity is a vector quantity having a magnitude and a direction, a change in the mass’ direction means that it is being accelerated. According to the second law of motion, acceleration occurs in the same direction as the applied force. The force, F_c, acting on the mass is always directed toward the center of the circle. Thus, the acceleration is also directed toward the center of the circle. This acceleration is called centripetal acceleration.

Uniform circular motion can be analyzed using vector diagrams to derive the equations for centripetal acceleration and centripetal force. Note that the centripetal force is proportional to the square of the velocity. Thus, doubling the speed of a moving object will require four times the centripetal force to keep the motion in a circle.

The characteristic parabolic curve observed in the accelerometer device is a reflection of the centripetal force gradient that is set up with the rotary motion. The greatest F_c is found at the outside of the circle where the radius (r) is the greatest. For the F_c to be greater, the water, which can flow easily, is “piled up” in the gradient mathematically depicted by the parabolic curve.