A crane is lifting a crate as shown. The weight of the crateis 300lb. For each o

Question

A crane is lifting a crate as shown. The weight of the crateis 300lb. For each of the following three cases calculate thetension force on the cable and for any case in which that tensionis not constant, plot the tension as a function of time fior thefirst 5 seconds of the lift (Ignore plot I will do this part once Iknow the equation) a. lifting at conatant velocity v=5ft/s straight up b. lifting such that velocity v-2t straight up, in ft/s when tis in seconds c. lifting such that v=t2 staright up, in ft/s whent is in seconds

Explanation / Answer

(a)   velocity constant,   acc =0          Tension = weightof crate = 300 lb . (b)    velocity =2t         acc = dv/dt =2      .            Tension = weight + ma =   weight + weight * a / g    =    300   +   300 * 2 / 32 =    319 lb . (c)    velocity =t2      acc = dv/dt = 2t     .               Tension = weight + ma =      300 +   300 * 2t /32     or .                     T =   300 + 18.75 t

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