Question

Force =dispalcement in vector form

Answer 1

Explanation:

How do we calculate work done if given in the vector form?

Which is the fastest scientific calculator for engineering?

You can it , as the other quantity are vector there dot product is scalar .there you can understand better.

w=∫⃗ F⃗ ⋅d⃗ r⃗

W=∫F∙dr

Hence you can calculate work done even if force and position given in position vector . Lets take an example ,

Consider a force F = 5xi+ 10yj and it change it position from origin to r = 2i + 5j , then work done is equal to :

W=∫⃗ ⃗ F⃗ ⋅⃗ d⃗ ⃗ r

W=∫((5xi+10yj)dr

w=∫((5xdx+10ydy))

w=∫₀²5xdx+∫₀⁵10ydy

w=[(5x²)/2]₀²+[(10y²)/2]₀⁵

w=[((5∗4)/2)−0]+[((10∗25)/2)−0]

w=[10]+[125]

w=135j

Hence, the work done under given circumstances is 135j

Answer 2

Answer:

In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.[1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position.