Question
Please slove the below mention question:
A) A uniform ladder of weight w rests on rough horizontal ground against a smooth vertical wall. The vertical plane containing the ladder is perpendicular to the wall and the ladder is inclined at an angle θ to the vertical. Prove that, if the ladder is on the point of slipping and µ is the coefficient of friction between it and the ground, then tanθ = 2µ
B) Two particles of mass 3 kg and 4 kg are connected by a light inelastic string passing over a smooth fixed pulley. The system is released from rest with the string taut and both particles at a height of 2 m above the ground. Find the velocity of the 3 kg mass when the 4 kg mass reaches the ground, and find when the 4 kg mass reaches the ground.
C) A box of mass 14 kg is placed in the back of a van. The coefficient of friction between the box and the floor is 0.5. What happens to the box if the lorry moves off with an acceleration of
(a) 4 ms-2
(b) 5 ms-2
(c) 8 ms-2
(Take g = 10 ms-2)
Can i get answer before 3pm today. Please i request you to help me out from the issue...
(a)let R and N are reactions by the ground and wall then for equilibrium
μR = N
R = w
and about ground point
N*lcosθ = w*lsinθ/2
now solve
(b) 4g-T = 4a
T-3g = 3a
solve for a
use h = 0t+1/2at2 for getting t
and v = 0 +at for v
(c) for a = 8 pseudo force = 14*8 and friction max = 0.5*14*10 so box will fall in backward direction