Question

Question #90693

Answer 1

Recall the Newton' second Law of motion for an object of mass `m` acted upon a force `vecF`
`vecF=mveca` ......(1)
where `veca` is the acceleration produced.

If a force acts through a displacement `vecs`,
Work done `W=vecFcdot vecs` .....(2)
Using (1) we can write (2) as
`W=mvecacdot vecs` ....(3)

Recall the kinematic equation
`vecv^2-vecu^2=2vecacdot vecs` .....(4)
where `vecu` is the initial velocity, `vecv` is the final velocity.

Using (4) equation (3) becomes*
`W=1/2m(vecv^2-vecu^2)`
Inserting given values
`W=1/2xx8.1((9.6hati+2.3hatj)^2-(9.9hati+6.0hatj)^2)`
We know that square of a vector is dot product of vector with itself hence, above equation becomes
`W=1/2xx8.1((9.6^2+2.3^2)-(9.9^2+6.0^2))`
`=>W=-148.1J`

*recall that equation is `W=("Final kinetic energy"-"Initial Kinetic energy")`