Determine the normal force the `10 kg` crate `A` exerts on the smooth cart `B` , if the cart is given an acceleration of `a = 2 m//s^(2)` down the plane . Also find the acceleration of the crate . Set `theta = 30^(@) (g = 10 m//s^(2))`

Explanation

Free body diagram of crate `A` w.r.t. ground is shown in figure

equation of motion is
`100 - N = 10a_(A)` …(i)
`a_(A) = a sin 30^(@) = (2) ((1)/(2))` or `a_(A) = 1 m//s^(2)`
Substituting in Eq. (i) , we get
`N = 90 N`