PHY Mechanics Supplemental Problem For lower objectspeeds, the drag force acting

Question

PHY Mechanics Supplemental Problem

For lower objectspeeds, the drag force acting on an object is directly proportionalto the velocity of

Here,b is also referred to as the drag coefficient (butit has different units than the drag coefficient we

discussed in class dueto the different functional form of the force). The negative signtells us that the

drag force is alwaysdirected in the direction opposite the object’s instantaneousvelocity.

Suppose a 2.0 kgobject is dropped from a high altitude (though low enough that theacceleration due

to gravity can stillbe considered to be the same as the surface value within measurablelimits) and that

the value of the dragcoefficient is 0.75 kg/s.

(a) What is theterminal speed of this object?

(b) What is thespeed of the object at t = 3.0s after it is dropped?

Explanation / Answer

a) Formula for calculating the value of the terminal speed of theobject is                  v = (mg) / b Here m = 2.0 kg           g =9.8m/s2           b =0.75 kg/s b) Given that Initial speed (u) of the object is zero. When the ball is falling downwards, then             mg - D = ma             mg - bvt = ma               g - (b/m)vt = a               g -(b/m)vt = (v - u)/t                               = (v - 0)/t                               = v/t                            v= gt - t(b/m)vt .................. (1) Here g = 9.8m/s2           t =3.0s           b= 0.75 kg/s         vt is substituted here which is calculated fromthe part (a)           t =3.0s           b= 0.75 kg/s         vt is substituted here which is calculated fromthe part (a) Substitute all these values in the eq (1) we get the requiredvalue. c) Formula for calculating the value of the distance traveled bythe object is             S = ut + (1/2)at2                  = 0 + (1/2)at2                  = (1/2)at2                  = (1/2)(v - u)t Here u = 0           v issubstituted here which is calculated from the part(b).              

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