Impulse and Ground Reaction Forces (GRF)

In class, you have been introduced to the relationship that exists between ground reaction forces (GRF), force, time, impulse and velocity. Newton's second law (F = m a) can be written in a form which includes the definition of acceleration:

F = m (Δ v / Δ t)

With simple algebraic rearrangement, this can be written as:

F Δ t = m Δ v or

Impulse = Change of Momentum

The "Impulse" part of this expression is a new quantity in our study of mechanics. It depends on both force and the time over which the force was applied. Units of impulse involve force and time: (Newtons * seconds). This impulse-momentum relationship is an important means of determining what motion results from an applied force. In the case of constant force application, impulse is particularly easy to calculate (see Figure 1). However, if force is not constant (which is typical of most real situations) a slightly different approach must be used as shown in Figure 2.

Since the impulse is essentially the area under the force-time curve, it can be approximated by a series of rectangles. Each rectangle would represent the impulse over the time interval Δ t.

Each area is calculated by taking the average force over a time interval (Δ t) and computing and multiplying it by Δ t:

Area of rectangle = ((F1 + F2)/2) * Δ t

The purpose of this lab will be to estimate the horizontal and vertical impulse associated with the impact of the front wheel of a mountain bike with a bump using the concept described above. With the data set provided to you, you will:

• Graph the horizontal force data sets vs time on ONE graph.
  
• Graph the vertical force data sets vs time on ONE graph.
  
• For each fork, determine the maximal horizontal and vertical braking force using a function in excel.
  
• For each fork, determine the horizontal braking impulse using the approximation technique described above.
  
• For each fork, determine the change in horizontal velocity (Δ v) associated with the impact if the mass of (rider + bike) was 90 kg. Show how Δ v was calculated. Based solely on the changes in velocity found for each fork, which fork would you want to have on your bike? Explain.
  
• For each fork and assuming that horizontal and vertical maximal forces occurred at the same time, determine the angle (in degrees) of the resultant maximal reaction force which is applied by the bump to the wheel. Remember that MS Excel calculates angles in radians. Make the appropriate conversions.

SUMMARY REPORT

Based on your calculations, briefly summarize, in your own words, the methodology and results of this experiment. Make sure to hand in your graphs and spreadsheets, along with an explanation of your calculations and a conclusion regarding the suspension fork performance. Your spreadsheet should fit on a single page! Use the formatting options for this task. Limit your writing to three pages double-spaced.