Determine the force to pull box along a level surface:

A metal box having weight 10KN is pulled along a level surface at the uniform speed by applying horizontal force of 3500N. If another box of 6KN is put on the top of this box, determine the force needed.

Sol.: In first case as shown in the given figure

∑H = 0

µ R = 3500                                                                                                                               ...(i)

∑V  = 0

R = W = 10KN = 10000                                                                                                 ...(ii)

Putting value of R in the equation (i)

µ = 0.35                                                                                                                             ...(iii)

Now consider second case: as shown in the figure

Now the normal reaction is N1,

∑H = 0

P - µR1 = 0

P = µ R1                                                                                                        ...(iv)

∑V = 0

R₁ = W = 10KN + 6KN = 16000

R₁ = 16000                                                                                                                           ...(v)

Putting value of R₁ in the equation (iv)

P = 0.35 × 16000

P = 5600N                                                                   .......ANS