an object moves along a straight line from (3,2,-6) to (14,13,9) when a uniform force F=4i^+j^+3k^ acts on it . find the work done and the angle between the force and displacement. Please give me complete solution
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Answer:
An object moves along a straight line from 3i+2j+6k to 14i+13j+9k when a uniform force F=4i+j+3k acts on it. What is the work done and the angle between force and displacement?
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An object moves along a straight line from 3i+2j+6k to 14i+13j+9k when a uniform force F=4i+j+3k acts on it. What is the work done and the angle between force and displacement?
a = 3i+2j+6k [?] ; b=14i+13j+9k [?] ; F=4i+j+3k [?]
∆ab = b - a = 11i+11j+3k ; W = ? ; angle(F;∆ab)=?
W = F•∆ab = 4*11+1*11+3*3= 64 [??]
cos(angle) = u_F • u_∆ab
u_∆ab = ∆ab/|∆ab| = (11i+11j+3k )/√(11^2+11^2+3^2) = 0.694i + 0.694j+0.189k
u_F = F./|F| =4i+j+3k / √(4^2+1^2+3^2)=
(4/√26)i + (1/√26)j + (3/√26)k
cos(angle) = u_F • u_∆ab
= (1/√26)(0.6941*4+0.6941*1+0.189*3)
= 0.7918188956 ,
angle(F,∆ab) = acos(0.7918188956) =37.644°