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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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Most popular questions from this chapter

Figure 12-19 shows an overhead view of a uniform stick on which four forces act. Suppose we choose a rotation axis through point O, calculate the torques about that axis due to the forces, and find that these torques balance. Will the torques balance if, instead, the rotation axis is chosen to be at

(a) point A(on the stick),

(b) point B(on line with the stick), or

(c) point C(off to one side of the stick)?

(d) Suppose, instead, that we find that the torques about point Odoes not balance. Is there another point about which the torques will balance?

Figure 12-49ashows a vertical uniform beam of length Lthat is hinged at its lower end. A horizontal forceFa鈫� is applied tothe beam at distance yfrom the lower end. The beam remainsvertical because of a cable attached at the upper end, at angle胃with the horizontal. Figure12-49agives the tension Tin the cableas a function of the position of the applied force given as a fraction y/Lof the beam length. The scale of the Taxis is set byTs=600N.Figuregives the magnitude Fhof the horizontal force on thebeam from the hinge, also as a function of y/L. Evaluate (a) angle胃and (b) the magnitude of Fa鈫�.

A tunnel of length L=150 m, height H=7.2 m, and width 5.8 m (with a flat roof) is to be constructed at distance d=60 m beneath the ground. (See the Figure.) The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 960 cm2. The mass of 1.0 cm3 of the ground material is 2.8 g. (a) What is the total weight of the ground material the columns must support? (b) How many columns are needed to keep the compressive stress on each column at one-half its ultimate strength?

In Fig. 12-44, a 15 kg block is held in place via a pulley system. The person鈥檚 upper arm is vertical; the forearm is at angle胃=30o with the horizontal. Forearm and hand together have a mass of 2.0 kg, with a center of mass at distance d1=15鈥塩尘from the contact point of the forearm bone and the upper-arm bone(humerus). The triceps muscle pulls vertically upward on the forearm at distanced2=2.5鈥塩尘 behind that contact point. Distanced3is 35 cm. What are the (a)magnitude and (b) direction (up or down) of the force on the forearm from the triceps muscle and the (c) magnitude and (d) direction (up or down) of the force on the forearm from the humerus?

In Fig 12-66, asphere is supported on a frictionless plane inclined at angle 胃=45掳from the horizontal. Angle 蠒is 25掳. Calculate the tension in the cable.
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