Question

4) Bubba pulls two boxes across the floor of his barn. One box has a mass (m1) of 20.4 kg and has a coefficient of kinetic friction of 0.321 with respect to the floor. The second box has a mass (m2) of 23.1 kg and a coefficient of kinetic friction of 0.177 with respect to the floor. The two boxes are connected with a rope. Bubba pulls on another rope connected to the second box. All of the ropes are horizontal. What is the tension in each rope if Bubba is pulling the boxes at constant speed?

Answer 1

กา potlin Free Body Dram Box One 2.

Gravitational acceleration = g = 9.81 m/s²

Mass of box 1 = m₁ = 20.4 kg

Mass of box 2 = m₂ = 23.1 kg

Coefficient of friction of box 1 with the floor = $\mu$₁ = 0.321

Coefficient of friction of box 2 with the floor = $\mu$₂ = 0.177

Tension in the rope connected between the boxes = T₁

Tension in the rope being pulled by Bubba and connected to box two = T₂

The boxes are moving are constant speed, therefore there is no acceleration which means all the forces are balanced.

From the free body diagram of the first box,

N₁ = m₁g

f₁ = $\mu$₁N₁ = $\mu$₁m₁g

T₁ = f₁

T₁ = $\mu$₁m₁g

T₁ = (0.321)(20.4)(9.81)

T₁ = 64.24 N

From the free body diagram of the second box,

N₂ = m₂g

f₂ = $\mu$₂N₂ = $\mu$₂m₂g

T₂ = T₁ + f₂

T₂ = 64.24 + (0.177)(23.1)(9.81)

T₂ = 104.35 N

Tension in the rope connecting the boxes = 64.24 N

Tension in the rope Bubba is pulling connected to box two = 104.35 N