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A particle is moved from (0,0) to ( a, a) under a force F=(3i vector +4j vector ) from 2 paths op , oqp what is the work done in these paths

A particle is moved from (0,0) to ( a, a) under a  force F=(3i vector +4j vector ) from 2 paths  op , oqp what is the work done in these  paths

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Grade:12

2 Answers

Venkat
273 Points
5 years ago
Work done = Force x distance = W =\vec{F}\cdot \vec{d} (dot product of force vector and distance vector)
WDOP
W_1=(3\vec{i}+4\vec{j})\cdot ((a,0)-(0,a)) \\W_1=(3\vec{i}+4\vec{j})\cdot (a,a) \\W_1=(3a+4a)=7a
 
WDOPQ
W_2=W_{OQ}+W_{PQ} =\vec{F}_x\cdot d_x+\vec{F}_y\cdot d_y \\W_2=(3\vec{i})\cdot (a)+(4\vec{j})\cdot (a) \\W_2=(3a+4a)=7a=W_1 \\W_2=W_1
Hence, choose option (A).
 
Venkat
273 Points
5 years ago
A particle is moved from (0,0) to ( a, a) under a  force F=(3i vector +4j vector ) from 2 paths  op , oqp what is the work done in these  paths
there is a typo error. read distance vector as distance...
 

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