In the previous example, suppose we move the block by pulling it with the help of a massless string tied to the block as shown here. What is the force F required to produce the same acceleration in the block as obtained in the last example ? (Given m=3kg,mu_s=0.3,mu_k=0.25 ,theta=37,a=8.4m/s^2)

Explanation

We are given that,
`m = 3kg, mu_(s) = 0.3, mu_(k) =0.25, theta = 37^(@)` and `a = 8.4 ms^(-2)`
In order to determine the force F, we first draw the FBD as shown below
The equations of motion therefore, are `N + F sin theta = mg `
`N = mg - F sin theta `
`F cos theta -f = ma ` and where `f = mu_(s)N ` before the start of the motion, once motion is set,`f mu_(k) N `.

Hence, force F which produces `a = 8.4 m//s^(2)` is given by `F cos theta - mu _(k) (mg -F msin theta ) = ma `
or `F = ( ma+ mu k m g )/( cos theta + mu k sin theta ) `
`= ( 3 (0. 4+0.25 xx 9.8))/(0.8 + 0.25 xx 0.6 ) = 34.26N`