Velocity and work?
When a body is acted upon a force of ( 5 i ^ + 4 j ^ − 3 k ^ ) N , it begins to move with a constant velocity of ( 2 i ^ − 3 j ^ − 7 k ^ ) m/s . Find the work done(in joules) by the force after 4 seconds.
The answer is 76.00.
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1 solution
Nice solution.. but can we do it directly without finding the power ? W = F ⋅ s ⟹ W = ( F ⋅ v ) × t
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No, that makes f,v,t scalar product :P It works if we calculate the dot product first and then multiply the numerical answer we obtain with the numerical time.
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Easy one but it's Level 3 :)
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@Abhiram Rao – Thanks! Dont worry about the level, it automatically changes with the number of correct answerers :)
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@Ashish Menon – The first Level 4 Classical Mechanical Problem I solved :)
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@Abhiram Rao – brilliant is an excellent place to learn , diverse and beautiful minds from all over the place will help you to develop your skills , soon you will be able to solve level 5 problems as well :)
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@Ujjwal Mani Tripathi – Very inspiring :)
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@Ashish Menon – thank you , i shared my experience i have been on brilliant since 4 years from the right start , in the starting i was on level 2 in all the topics but continuous learning helped me level up my maths , by the way your physics questions are cool .
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@Ujjwal Mani Tripathi – Thanks, so you are a very old user, nice to meet you.
@Abhiram Rao – Congrats!!
@starwar clone Thanks a lot for your advice! And @Ashish Siva How are you ? Been a very long time
My doubt is can we find displacement by s(vector)=v(vector) x time then W =F.s ??
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Well since time has no i ^ , j ^ and k ^ you might be asking to multiply the magnitude of the velocity vector and obtain the magnitude of the displacement vectorw. Well, I am not sure that qill work becayse it corresponds(likely) to cross product but we need the dot product. The last time I tried that methid I failed. But, the answer is always correct if you go for the dot product of F and S directly. So, I would suggest you to do the same.
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Yes exactly i too failed. That's why i asked the doubt.
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@Jus Jaisinghani – Hehe, wierd stuff right? I lost 5 marks in exam when i tried somwthing "fancy" for the first time :P
@Jus Jaisinghani – Here is one relevant problem for this topic I posted.
I did the same and got correct answer. s(vector) = (8,-12,-28)
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ya bro i got my silly mistake :) and then got it correct
P ∴ W = F ⋅ v = ( 5 i ^ + 4 j ^ − 3 k ^ ) ⋅ ( 2 i ^ − 3 j ^ − 7 k ^ ) = 1 0 − 1 2 + 2 1 = 1 9 watts = P × t = 1 9 × 4 = 7 6 . 0 0 J