Question

what constant horizontal force is required to drag of 5 kg block along the horizontal surface with an acceleration of 1 metre per second if the coefficient of sliding friction between the block and the surface is 0.5​

Answer 1

       $\text{\huge \bf \underline{Answer:}}$

       $\text{The FBD of the block is given in the attachment}$

       $\text{It is given that:}$

       $\text{Acceleration of body}(a) = 1 \text{ ms}^{-2}$

       $\text{Coefficient of kinetic friction}(\mu_k) = 0.5$

       $\text{Mass of body}(m) = 5 \text{ kg}$

       $\text{Acceleration due to gravity}(g) = 10 \text{ ms}^{-2}$

       $\text{We have to find the value of external force}(F)\text{ for}\\\text{which the given is possible}$

       $\text{Since, there is no movement of the body in }y \text{ - }axis$

$\implies F_y = 0$

$\implies N - mg = 0$

$\implies N = mg$

$\implies \text{Normal Force}(N) = mg = 50 \text{ N}$

       $\text{We know that frictional force}(f) = \mu_k \times N$

$\implies f = 0.5 \times 50 = 25 \text{ N}$

       $\text{Now we study the movement on }x\text{ - }axis$

$\implies F_x = ma$

$\implies F - f = ma$

$\implies F - 25 = 50 \times 1$

$\implies F - 25 = 50$

$\implies F = 50 + 25$

$\implies \boxed{\boxed{F = 75 \text{ N}}}$