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Chapter 6: Q.41 (page 156)

An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.41, and does not touch the bed.

a. Determine the amount of tension in the rope by using Newton鈥檚 laws to analyze the hanging mass.

b. The net traction force needs to pull straight out on the leg. What is the proper angle胃for the upper rope?

c. What is the net traction force pulling on the leg?

Short Answer

Expert verified

a. Tension in rope = 58.8N

b. Proper angle 胃for the upper rope = 67.5掳

c. Net traction force pulling on the leg = 79.0N

Step by step solution

01

- Tension

Tension Force : - Force that is transmitted through the a rope, string or wire when pulled by forces acting from opposite sides.

02

- Given

Mass of foot and boot = 4.0kg

Hanging mass = 6.0kg

Angle(胃) = 12掳

03

Step 3

a. The amount of tension in rope : -

鈭� Fy = T鈭扢g =0

M = mass of the hanging weight

T = Mg

=6.0脳9.81

T =58.8 N

04

Step 4

b. 鈭�Fy = T sin胃- T sin 12掳-mg = 0

Solving for the angles

胃= sin鈭�1 Tsin12掳+mgT

T = Mg

胃= sin鈭�1 role="math" localid="1647584331124" sin12掳+mM

胃= sin鈭�1 0.027+46.0

胃= sin鈭�1 (0.873)

胃= 60.80掳

05

Step 5

鈭�Fx = T cos 60.80掳 + T cos 12掳 鈭� Ffraction=0

Ffraction= T (cos 60.80掳 + cos 12掳)

= 58.8 (0.487 + 0.978)

Ffraction= 86.14N

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