Suppose Bob tightens in a bolt using 35N of force at a 30 degree degree angle on

Question

Suppose Bob tightens in a bolt using 35N of force at a 30 degree degree angle on his 0.4m wrench, and Joe tightens a bolt using 20N of force at a 60 degree degree angle on his 0.7m wrench. If it is 72 degree degrees (F) outside, then who did more work? You blow on a small toy sailboat floating in your bathtub. You start with your lips poised at (1, 3, 4) while the boat is at (2, 2, 0). While you blow, you do not change your blowing vector as you follow the boat. If your toy sailboat was sophisticated enough to measure the work of its movement as 10J and it ended at position (6, 2, 0), then what was the force of your breath?

Explanation / Answer

1)

for work done by bob:

F=35, r=0.4,=30o

torque,T=Frsin

T=35*0.4*sin30o

T=7

work =T*

work =7*(30o/180o)*

work =3.665

for work done by joe:

F=20, r=0.7,=60o

torque,T=Frsin

T=20*0.7*sin60o

T=73

work =T*

work =73*(60o/180o)*

work =12.6966

so joe did morework

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2)

direction of force =<2-1,2-3,0-4> =<1,-1,-4>

unit vector in direction of force =<1/(12+(-1)2+(-4)2),-1/(12+(-1)2+(-4)2),-4/(12+(-1)2+(-4)2)>

unit vector in direction of force =<1/18,-1/18,-4/18>

let magnitude of force =f

force vector,F =f<1/18,-1/18,-4/18>

direction vector of boat movement,d =<6*2,2-2,0-0> =<4,0,0>

work=|F.d|

=>|f<1/18,-1/18,-4/18>.<4,0,0>| =10

=>f[((1/18)*4)+((-1/18)*0)+((-4/18)*0)]=10

=>f(4/18)=10

=>f=(1018)/4

=>f=10.6066

magnitude of force of your breath is 10.6 newton

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