Supplement to High school physical science . avity, mxg dynes, acting verti- cally downward. (b) The tension of the string, T dynes, acting vertically upward. ITdynes ^Tdynes Therefore, since ml is descending, theresultant of the forces actingon mx = (mi9 - T) this force is also mxa , mxg — T = m^ T = ra1#-ra1a (1) (2) Consider the forces acting on m2. These are (a) Gravity, m2g dynes, acting vertically downward.(6) The tension of the string, T dynes, acting verticallyupward. Therefore, since m2 is ascending, the resultant of the forcesacting on m2 = (T - m^g)
Supplement to High school physical science . avity, mxg dynes, acting verti- cally downward. (b) The tension of the string, T dynes, acting vertically upward. ITdynes ^Tdynes Therefore, since ml is descending, theresultant of the forces actingon mx = (mi9 - T) this force is also mxa , mxg — T = m^ T = ra1#-ra1a (1) (2) Consider the forces acting on m2. These are (a) Gravity, m2g dynes, acting vertically downward.(6) The tension of the string, T dynes, acting verticallyupward. Therefore, since m2 is ascending, the resultant of the forcesacting on m2 = (T - m^g) this force is also m2<x T - m^g — m0a or T = + m2a (2) But T = m1g-m1a (1) above. Hence mxg — m^a = m„g + m0a m, - ra0 mx + m2 g cm. per sec. per cm. 10 SUPPLEMENT TO HIGH SCHOOL PHYSICAL SCIENCE. and Cm, - nO 2m1??i2 g dynes. mx + to2 3. Two bodies, of masses mx grams and m2 grams, are con-nected by a light inextensible string; to, is placed on a roughplane inclined at an angle 0 to the horizon, and the string. T Dynes Vm^ff Dynes Fig. 3. after passing over a small smooth pulley at the top of theplane (Fig. 3), supports mv which hangs vertically. If thecoefficient of friction of the plane is fx., and tox descends, deter-mine (1) the acceleration of the system, (2) the tension of thestring. Let T dynes be the tension of the string and a the accelera-tion of the masses. Now, considering the forces acting on mvwe have, as in examples 1 and 2 above, T = m1g-m1a . (1) Consider the forces acting on to2. These are (a) Gravity, m0g dynes, acting vertically downward. (b) Normal pressure, acting at right angles to the plane upward. Let this be R. dynes. (c) Tension of the string, T dynes, acting along the plane upward. THE METRIC UNITS OF FORCE. 11 (d) Friction, F. ?= /x R dynes, acting along the plane down-ward (since the mass is moving upward).Resolve these forces along the plane and at right anglesto it. Then if X denote the algebraic sum of the componen
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