EXAMPLE PROBLEM 1.2 GIVEN: Ball, m= 0.2 kg. released from rest at yo =500 m Air resistance, Fp kv, where k=2x10N.s/m2 Units: FD(N), V(m/s) FIND: (a) Speed at which the ball hits the ground (b) Ratio of speed to terminal speed SOLUTION: tion:>F Assumption:(1) Neglect buoyancy force The motion of the ball is governed by the equation S F= may = n dv Since V- vo), we write >F> dv d dy dr y Then ∑F=FD-mg=kV一mg=m分 Separating variables and integrating nav dye kv-n In(kv2-mg) kva 二Pg Taking antilogarithms, we obtain kV-- mg mg s(->o) Solving for v gives 一("(1-c20m
Substituting numer rical values with y=0 yields 1n2 02kg9.81m N -500 322×10-4N·s2k V=78.7m/s V At terminal speed, ay =0 and 2F=0=kV2-mg 12 Then,v,=mepla 2 02kg9.81m N =99.0m/s. k s22×10-4N·s2kgm The ratio of actual speed to terminal speed is V78.7 V =0.795,or79.5% V This problem is included as a reminder of the method of description used in particle mechanics and to introduce a variable aerodynamic drag force
1-6 Dimension and Unit The physical quantities of engineering problems include units length, time, mass and temperature as dimension The primary quantities(length, time, mass, and temperature as dimension )and secondary quantities(dimensions are expressible in terms of the dimension of the primary quantities)
1-6 Dimension and Unit • The physical quantities of engineering problems include units: length,time,mass, and temperature as dimension • The primary quantities(length,time,mass, and temperature as dimension )and secondary quantities (dimensions are expressible in terms of the dimension of the primary quantities)
1-6 Dimension and Unit 1-6. 1 System of Dimension a)mass(M), length (L), time(t) temperature(T)(MLtT) b) Force(F), length ( L), time(t) temperature(T)(FLtT c)Force(F), mass(M), length(L) time(t), temperature(T) (FMLtT)
1-6 Dimension and Unit • 1-6.1 System of Dimension • a) mass(M), length(L), time(t), temperature(T)(MLtT) • b) Force(F), length(L), time(t), temperature(T)(FLtT) • c) Force(F),mass(M) ,length(L), time(t), temperature(T) (FMLtT)
1-62 system of unit a SI, MLtt(primary) Secondary dimension unit of mass(kg) Force(N) length(meter) IN=lkg. m/s time(second)s temperature(kelvin)v absolute metric 1 dyne=l g cm/s2 system of unit
1-6.2 system of unit • a. SI, MLtT(primary) unit of mass(kg) length (meter) time (second) s temperature (kelvin) Absolute metric system of unit Secondary dimension Force(N) 1N=1kg. m/s2 1dyne=1.g.cm/s2