Question

An object with a mass of `3 kg` is acted on by two forces. The first is `F_1= < 2 N , 8 N>` and the second is `F_2 = < -1 N, -3 N>`. What is the object's rate and direction of acceleration?

Answer 1

`a=sqrt(26)/3" "m/s^2`

Explanation:

`1-"Find the composition of the two vectors"`

`F_1= <2,8 >" ; "vec F_1=<2i+8j`
`F_2= <-1,-3 >" ; "vec F_2=-i-3j`
`vec F_R:"composition of the two vectors"`
`vec F_R=(2-1)i+(8-3)j" ; "vec F_R=i+5j`

`2-"Find the magnitude of " F_R`
`||F_R||=sqrt(1^2+5^2)=sqrt(1+25)=sqrt26`

`3-"Find acceleration of this object using Newton's second law"`

`a=(||F_R||)/m`

`a:"represents acceleration of the object"`
`m:"represents mass of the object"`

`a=sqrt(26)/3" "m/s^2`

`4-"The direction of object moving is being shown in the animation"`