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Physics from a Croquet Mallet and Ball

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Submitted by Rich on Sat, 01/19/2019 - 20:23

Introduction

Various forms of the sport now known as croquet have been around for centuries.  Plastic or wooden balls are struck with a mallet through hoops, called wickets in the United States.  The components of a typical croquet set are shown in Figure 1.  Very popular in the UK, there is even a World Croquet Federation for those who take the sport seriously.  In the United States, it is common to set up croquet as a garden game at graduation and birthday parties.  But who would have thought that a croquet ball and mallet equipped with PocketLab Voyager and the PocketLab app could form the basis for a study of many concepts of physics--Newton's 2nd and 3rd Laws of Motion, conservation of energy, force, momentum, impulse, velocity and acceleration.  In accordance with NGSS practices, this lesson provides a lab challenging physics students to design an experiment that allows a quantitative study of these concepts.

Croquet Set Components
Figure 1 - Croquet Set Components

Suggested Setup for This Physics Lab

Voyager is mounted to a croquet mallet with strong mounting tape, as shown in Figure 2.  Masking tape is used to secure the orange cover to Voyager so that it will not pop off when the mallet strikes the croquet ball.

Closeup of Voyager mounted to a croquet mallet
Figure 2 - Voyager Mounted to a Croquet Mallet

We need to come up with some way to control the speed of the mallet when it hits the ball on repetitive strikes of the ball.  We also want a way to easily determine this speed. Figure 3 shows the author's approach.  The croquet mallet becomes a pendulum that swings on a metal rod that has been loosely inserted into a hole drilled into the handle of the mallet.  The metal rod is supported by a pair of ring stands that are clamped to the table or weighted at the base to provide stability when the croquet mallet is allowed to swing.

Closeup of the front of the lab setup
Figure 3 - Croquet Mallet as a Pendulum

Figure 4 shows the complete croquet physics lab setup.  The croquet ball is placed near the right side of the mallet.  The mallet is raised to the left so that the mallet's handle is horizontal, it is released, and then strikes the croquet ball.  Always releasing the mallet when the handle is horizontal will keep the speed of the mallet just before impact with the ball the same.  Voyager's accelerometer measures the mallet's acceleration  when it strikes the ball.  A meter stick is placed parallel to the path of the ball after being struck by the mallet.  A frame-by-frame video analysis of the ball moving to the right can be used to determine the speed of the ball after impact from the mallet.  A cushion at the far right of Figure 4 is used to keep the ball from rolling off the table.  Alternatively, a student could catch the ball when it rolls off the table.  

Complete croquet physics lab setup
Figure 4 - Complete Croquet Physics Lab Setup

Combined PocketLab Data/Video Example

The following video is an example from a typical run during this lab.  White tabs of paper were placed 10 cm apart along the length of the meter stick as the video clarity was not adequate to read the meter stick directly.

The Croquet Physics Challenge

Using only Voyager's accelerometer, a meter stick, a balance for measuring mass, and a combined data/video from the PocketLab app, the student's job is to determine the following things:

  1. The speed of the mallet just before striking the croquet ball.
  2. The maximum acceleration of the mallet during impact with the croquet ball.
  3. The maximum force on the mallet during impact with the ball.
  4. The maximum force on the ball during impact with the mallet.
  5. The maximum acceleration of the ball during impact with the mallet.
  6. The speed of the croquet ball following impact with the mallet.
  7. The amount of time during actual impact of the mallet and croquet ball.

For each of the above items, be sure to address any assumptions you are making and indicate any laws of physics or physics principles that you are using.  Provide any spreadsheets/graphs/videos that you used to support your work.

A Similar Lab with a Pendulum Impacting a Cart

Click this link for a similar experiment that uses a pendulum impacting a physics cart.

Croquet Mallet Equipped with PocketLab Voyager
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