Question

Three blocks are in contact with one another on a fric-tionless, horizontal surface as shown in Figure P5.54. Ahorizontal force is applied to m1. Take m12.00 kg, m23.00 kg, m34.00 kg, and F18.0 N. Draw a separatefree-body diagram for each block and find (a) the acceler-ation of the blocks, (b) the resultantforce on each block,and (c) the magnitudes of the contact forces between theblocks. (d) You are working on a construction project. Acoworker is nailing plasterboard on one side of a lightpartition, and you are on the opposite side, providing“backing” by leaning against the wall with your back push-ing on it. Every hammer blow makes your back sting. Thesupervisor helps you to put a heavy block of woodbetween the wall and your back. Using the situation ana-lyzed in parts (a), (b), and (c) as a model, explain howthis change works to make your job more comfortable

Answer 1

P , P' = contact forces

a)

the three blocks move together , hence assuming the three blocks as one block

M = m₁ + m₂ + m₃ = 2 + 3 + 4 = 9 kg

F = applied force = 18 N

a = acceleration = F/M = 18 / 9 = 2 m/s²

b)

resultant force on m₁ = m₁ a = 2 x 2 = 4 N

resultant force on m₂ = m₂ a = 3 x 2 = 6 N

resultant force on m₃ = m₃ a = 4 x 2 = 8 N

c)

for block m₁ :    P = contact force

force equation can be given as

F - P = m₁ a

18 - P = 4

P = 14 N

for block m₃ :    P' = contact force

force equation can be given as

P' = m₃ a

P' = 8 N