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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 kg and is on a ramp at angle θ=30.0°box Bhas a mass of7.00 kg 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 N.
  2. Angle made by upper cord with the horizontal is 64.0°.

Step by step solution

01

Understanding the given information

Mass of box A,mA=11.0 kg

Mass of box B,mB=7.00 kg

Angle made by ramp to the horizontal,θ=30°

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.

Tcosθ=TAcos30°Tsinθ=TA×sin(30°)+TB

03

(a) Calculation for the tension in the upper cord

We have,for the equilibrium of forces,

Tcosθ'=TAcos30°Tcosθ'=mA×g×sin(30°)×cos(30°)           (1)

Also,

Tsinθ'=TA×sin(30°)+TBTsinθ'=mA×g×sin(30°)×sin(30°)+mB×g              (2)

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

T=106 N

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

θ'=64.0°

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Most popular questions from this chapter

Question: In Fig. 12-26, a uniform sphere of mass m = 0.85 m and radius r = 4.2 mis held in place by a massless rope attached to a frictionless wall a distance L = 8.0 cm above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall.

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