Lab 3: Force Measurement

"If I have seen further, it is by standing on the shoulders of giants".

Sir Isaac Newton, English mathematician and physicist

Introduction

In this lab the focus of study is vertical ground reaction force and subsequent linear motion of the center of mass of the body. Reaction Forces are equal and opposite to the forces applied by the body to the ground (Newton's 3rd law). In addition, Newton's 2nd law (F = ma) governs the resulting motion.

A force platform is a device which measures ground reaction force. It is a three-dimensional measuring device. However we will deal only with the vertical component of the ground reaction force. A free body diagram of the plate and a subject is illustrated below:

R + W = 0 if no movement

R = - W

R = - W + m a if movement present

R = - m g + m a

R = m (-g + a) with g = -10 m/s/s

where W is weight of subject, R is reaction force, m is mass of subject and a is acceleration of subject.

For the case in which a person is stationary on the plate, the two forces (W and R) must be equal in magnitude and opposite in direction. If the person starts to move upward (acceleration of CM is positive), then ma is positive and the ground reaction force will increase in magnitude. With initiation of a downward movement (negative acceleration of the CM), ma is negative and the ground reaction force will decrease below body weight.

In summary:if acceleration < 0 then R < W

if acceleration = 0 then R = W

if acceleration > 0 then R > W

Procedures

Each group of students (maximum 2 students per group. You can decide to do the lab on your own, of course!). You will perform the following maneuvers on the force platform while it monitors the vertical ground reaction force:

  1. Stand on the force platform with your hands on your hips. Abruptly squat and hold this position. From the squat, rapidly stand up without leaving the platform.
  2. With hands on hips from a squat position, perform a maximal vertical jump without counter movement.
  3. With hands on hips from an upright position, perform a maximal vertical jump with counter movement.

For each condition, you will have an output that will be stored in an Excel file. This file will be sent to your University email account. You will graph each condition on a separate graph and label the appropriate graphs with the following:

  1. Body Weight
  2. Squat Down (SD) and Stand Up (SU)
  3. Unweighting period (UN)
  4. Peak Force before takeoff (PF)
  5. Takeoff(TO)
  6. Duration of Flight (dt)
  7. Landing (L)

Based on your personal or group data, briefly summarize the methodology and results of this experiment. You can use one report per group, but recognize that you will both receive the same grade. Include responses to the following questions in your discussion. Limit this writing to two pages double-spaced. Attach your graphs to the printout and return these to your instructor at the beginning of the next lab meeting.

Interpret your force-time curve for the first maneuver: what was the effect of the squat down on the reaction force? What was the effect of the stand up? Why does the reaction force respond in this manner?

Discuss the differences in your force-time curves for the vertical jumps with and without counter movement.

For each vertical jump, determine your flight time. You will use these data to predict the height of the jump in a subsequent exercise