Question

The force was sampled at 100 kS/s (one hundred thousand samples per second), which corresponds to a sampling interval of 0.00001 seconds which is also 0.01 ms.

For this exercise, the impact will be considered to be happening whenever the magnitude of the force is at least 0.01 newtons (1 cN).

time (s)	Force (N)
0	0
0.00001	0
0.00002	0
0.00003	0
0.00004	0
0.00005	0
0.00006	0
0.00007	0
0.00008	0
0.00009	0
0.0001	0
0.00011	0
0.00012	0
0.00013	0
0.00014	0
0.00015	0
0.00016	0
0.00017	0
0.00018	0
0.00019	0
0.0002	0
0.00021	0
0.00022	0.00
0.00023	0.00
0.00024	0.00
0.00025	0.00
0.00026	0.00
0.00027	0.00
0.00028	0.00
0.00029	0.00
0.0003	0.00
0.00031	0.00
0.00032	0.00
0.00033	0.01
0.00034	0.01
0.00035	0.01
0.00036	0.02
0.00037	0.02
0.00038	0.03
0.00039	0.04
0.0004	0.05
0.00041	0.07
0.00042	0.09
0.00043	0.12
0.00044	0.15
0.00045	0.20
0.00046	0.26
0.00047	0.32
0.00048	0.41
0.00049	0.50
0.0005	0.61
0.00051	0.73
0.00052	0.92
0.00053	1.13
0.00054	1.30
0.00055	1.63
0.00056	1.76
0.00057	2.22
0.00058	2.54
0.00059	2.95
0.0006	3.13
0.00061	3.47
0.00062	3.96
0.00063	4.61
0.00064	4.90
0.00065	5.54
0.00066	6.06
0.00067	6.20
0.00068	6.85
0.00069	7.18
0.0007	7.29
0.00071	7.74
0.00072	7.54
0.00073	7.63
0.00074	8.53
0.00075	8.17
0.00076	8.01
0.00077	8.03
0.00078	7.57
0.00079	7.96
0.0008	7.16
0.00081	6.77
0.00082	6.97
0.00083	6.00
0.00084	5.86
0.00085	5.35
0.00086	5.15
0.00087	4.42
0.00088	4.07
0.00089	3.59
0.0009	3.29
0.00091	2.76
0.00092	2.59
0.00093	2.08
0.00094	1.91
0.00095	1.51
0.00096	1.31
0.00097	1.15
0.00098	0.90
0.00099	0.74
0.001	0.62
0.00101	0.51
0.00102	0.40
0.00103	0.30
0.00104	0.24
0.00105	0.19
0.00106	0.16
0.00107	0.12
0.00108	0.09
0.00109	0.07
0.0011	0.05
0.00111	0.04
0.00112	0.03
0.00113	0.02
0.00114	0.02
0.00115	0.01
0.00116	0.01
0.00117	0.01
0.00118	0.00
0.00119	0.00
0.0012	0.00
0.00121	0.00
0.00122	0.00
0.00123	0.00
0.00124	0.00
0.00125	0.00
0.00126	0.00
0.00127	0.00
0.00128	0.00
0.00129	0
0.0013	0
0.00131	0
0.00132	0
0.00133	0
0.00134	0
0.00135	0
0.00136	0
0.00137	0
0.00138	0
0.00139	0
0.0014	0
0.00141	0
0.00142	0
0.00143	0
0.00144	0
0.00145	0
0.00146	0
0.00147	0
0.00148	0
0.00149	0
0.0015	0

1. What is the amount of time that the impact has undergone? In other words, what is Δt? Answer in milliseconds, and to the fourth decimal place.

2. Find the average force during the impact. Answer in newtons, and to the fourth decimal place.

3. Compute the impulse by computing the product of the average force and the time interval. Answer in N ms (newton-milliseconds), and to the fourth decimal place.

4.

Compute the impulse by computing the area under force vs time chart during the impulse.

If the sampling rate is high enough and uniform, the easiest way to compute the area is to simply add up all of the y-values (values on the vertical axis) and then multiply that sum by the sampling interval.

Answer in N ms (newton-milliseconds), and to the fourth decimal place.

Answer 1

1.

We need to consider impact when it is more than 0.01N.

As per table it shows that it started at 0.00033 s (0.33 ms) and became zero again at 0.00118 s (1.18ms).

So, Delta t = 1.18 - 0.33 ms = 0.8500 ms ( equal to 0.00085 second)

2.

We can use MS excel to calculate average impact force from 0.33 ms to 1.17 ms (when impact force was greater than or equal to 0.01 N
Average impact force during this time = 2.6464 N

3.

Impulse = 2.6464 * 0.85 N-ms = 2.2494 N-ms

4.

It can be calculated in MS excel. As every sample is of 0.01 ms, we can multiply Force value of that sample by 0.01 ms and then all the Force* Sampling time values can be added (Note that force values from 0.01 ms to 0.32 ms and 1.18 ms to 1.5 ms values are ZERO)

Sum of Force* Sampling time = 2.2494 N-ms