Falling Body with Air Resist - Revision history

Milllo at 00:09, 6 May 2020

2020-05-06T00:09:53Z

2020-05-06T00:08:48Z

2020-05-06T00:08:35Z

2020-05-05T13:45:01Z

2020-05-05T13:38:18Z

2020-05-05T13:12:01Z

2020-05-05T13:10:19Z

2020-05-05T13:08:40Z

2020-05-05T13:07:24Z

2020-05-05T13:06:35Z

@@ Line 9: / Line 9: @@
 mdv/dt + kv = mg
-dv/dt + vk/m = g    <----Standard form
+'''dv/dt + vk/m = g'''    <----Standard form
 * find u = e<sup>∫k/mdt</sup> = e<sup>kt/m</sup>

@@ Line 5: / Line 5: @@
 mdv/dt = mg - kv
-# put into standard form:
+* put into standard form:
 mdv/dt + kv = mg

@@ Line 5: / Line 5: @@
 mdv/dt = mg - kv
-put into standard form:
+# put into standard form:
 mdv/dt + kv = mg
@@ Line 11: / Line 11: @@
 dv/dt + vk/m = g    <----Standard form
-find u = e<sup>∫k/mdt</sup> = e<sup>kt/m</sup>
+* find u = e<sup>∫k/mdt</sup> = e<sup>kt/m</sup>
-multiply by u:
+* multiply by u:
 e<sup>kt/m</sup>dv/dt + e<sup>kt/m</sup>vk/m = ge<sup>kt/m</sup>
-use product rule:
+* use product rule:
 d/dt(ve<sup>kt/m</sup>) = ge<sup>kt/m</sup>
-integrate both sides:
+* integrate both sides:
 ve<sup>kt/m</sup> + C<sub>1</sub> = mg/ke<sup>kt/m</sup> + C<sub>2</sub>
-solve for v:
+* solve for v:
 v = mg/k - (C<sub>1</sub> - C<sub>2</sub>)/e<sup>kt/m</sup>

@@ Line 41: / Line 41: @@
 when t goes to infinity, e<sup>-kt/m</sup> goes to 0 so the terminal velocity = mg/k
-The value of k depends on mass and shape, so it can be determined by measuring terminal velocity:
+The value of k depends on mass and shape and it can be determined by measuring terminal velocity:
 average terminal velocity of an 80kg person = 148mph = 66m/s so k = 80kg(9.8m/s<sup>2</sup>)/66 m/s = 11.8 kg/sec

← Older revision		Revision as of 13:38, 5 May 2020
Line 40:		Line 40:

	when t goes to infinity, e<sup>-kt/m</sup> goes to 0 so the terminal velocity = mg/k		when t goes to infinity, e<sup>-kt/m</sup> goes to 0 so the terminal velocity = mg/k
		+
		+	The value of k depends on mass and shape, so it can be determined by measuring terminal velocity:
		+
		+	average terminal velocity of an 80kg person = 148mph = 66m/s so k = 80kg(9.8m/s<sup>2</sup>)/66 m/s = 11.8 kg/sec

@@ Line 27: / Line 27: @@
 solve for v:
-v = mg/k - (C<sub>1</sub> + C<sub>2</sub>)/e<sup>kt/m</sup>
+v = mg/k - (C<sub>1</sub> - C<sub>2</sub>)/e<sup>kt/m</sup>
 v = mg/k - Ce<sup>-kt/m</sup>

← Older revision		Revision as of 13:07, 5 May 2020
Line 16:		Line 16:

	e<sup>kt/m</sup>dv/dt + e<sup>kt/m</sup>vk/m = ge<sup>kt/m</sup>		e<sup>kt/m</sup>dv/dt + e<sup>kt/m</sup>vk/m = ge<sup>kt/m</sup>
		+
		+	use product rule:

	d/dt(ve<sup>kt/m</sup>) = ge<sup>kt/m</sup>		d/dt(ve<sup>kt/m</sup>) = ge<sup>kt/m</sup>

← Older revision		Revision as of 13:06, 5 May 2020
Line 36:		Line 36:

	v(t) = (mg/k)(1-e<sup>-kt/m</sup>)		v(t) = (mg/k)(1-e<sup>-kt/m</sup>)
		+
		+	when t goes to infinity, e<sup>-kt/m</sup> goes to 0 so the terminal velocity = mg/k