An object with mass 60 kg moved in outer space. When it was at location < 14, -2

Question

An object with mass 60 kg moved in outer space. When it was at location < 14, -23, -6 > its speed was 18.5 m/s. A single constant force < 210, 500, -210 > N acted on the object while the object moved to location < 20, -28, -10 > m. What is the speed of the object at this final location?
final speed =  m/s

(b An ubject final spead - th mas 60 kg m ved in uw spece. When it was at location 14-23-6 its speed was 18.5 m s. As r le constant fur e 210 500-210 > N acted un t e ub ect while the ub ect moved to ca un20-2 10 > m W ets the s ed of the ub ect at this nal I cation? Additional Materials Section 8.4

Explanation / Answer

Given that,

m = 60 kg

location r1 = <14, -23 , -6> m

r2 = <20, -28 , -10> m

F1 = <210, 500 , -210> N

vi = 18.5 m/s

Path difference, r = r2 - r1

r = <6 , -5 , -4>

Work done by Force F,

W = F.r = (210, 500 , -210 ) . (6 , -5 , -4)

W = -400 J

lnitial energy, Ei = (1/2)mvi^2

Ei = (1/2)*60*(18.5)^2 = 10267.5 J

Final energy, Ef = 10267.5 - 400 = 9867.5 J

from energy conservation,

Ef = (1/2)mvf^2

where, vf = speed of obect at final location

9867.5 = (1/2)*60*vf^2

vf = 18.13 m/s

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