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Chapter 12: Q83P (page 353)

Figure 12-84 shows a stationary arrangement of two crayon boxes and three cords. Box Ahas a mass of11.0鈥塳驳 and is on a ramp at angle 胃=30.0掳box Bhas a mass of7.00鈥塳驳 and hangs on a cord. The cord connected to box Ais parallel to the ramp, which is frictionless. (a) What is the tension in the upper cord, and (b) what angle does that cord make with the horizontal?

Short Answer

Expert verified
  1. Tension in the upper cord is106鈥塏.
  2. Angle made by upper cord with the horizontal is 64.0掳.

Step by step solution

01

Understanding the given information

Mass of box A,mA=11.0鈥塳驳

Mass of box B,mB=7.00鈥塳驳

Angle made by ramp to the horizontal,胃=30掳

02

Concept and formula used in the given question

Using the concept of equilibrium of forces, you can find the tension in the upper cord and the angle made by that cord with the horizontal. The equations used are given below.

Tcos胃=TAcos30掳T蝉颈苍胃=TA脳sin(30掳)+TB

03

(a) Calculation for the tension in the upper cord

We have,for the equilibrium of forces,

Tcos胃'=TAcos30掳T肠辞蝉胃'=mA脳g脳sin(30掳)脳cos(30掳)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�(1)

Also,

T蝉颈苍胃'=TA脳sin(30掳)+TBT蝉颈苍胃'=mA脳g脳sin(30掳)脳sin(30掳)+mB脳g鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆�夆�夆��(2)

Now, solving eq. (1) and (2), for tension we get

T=106鈥塏

04

(b) Calculation for the angle does that cord make with the horizontal

Solving the above eq. (1) and eq. (2), for angle we get

胃'=64.0掳

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