What is the tension in the upper string, physics, Basic Statistics

Question: The weights shown in the figure are in equilibrium. It consists of objects held by vertical strings. The object 3 weighs 1.4 N. The horizontal bars are identical, uniform and each weighs 0.5 N. What is the tension in the upper string?

 

1307_tension.png

Given that the weight of the object 3, W3 = 1.4 N The lower rod is in equilibrium. It means the net force and the net torque (i.e., moment of forces) acting on it is zero. The moment of the weights of object 2 and 3 are equal in magnitude

and opposite in direction (counterclockwise for W2 and clockwise for W3). The weight of this rod (W = 0.5 N) does not produce any torque about the point of suspension as it coincides with the center of gravity of the rod. Hence, from moment equation,

W2xL/2  - W3XL/2 = 0 

This gives, W2 = W3 = 1.4 N

Tension in the string connecting the upper and lower rods is given by T1 = W2 + W + W3 = 1.4 + 0.5 + 1.4 = 3.3 N (it follows from the fact that net force = 0)

The upper rod is also in equilibrium. It means the net force and the net torque acting on it is also zero. The upper rod is not suspended from its center of gravity. Hence, the weight of this rod (W = 0.5 N) also produces a counterclockwise torque about the point of suspension. The two points are different for this rod. Tension T1 acts downward on this rod and hence produces

clockwise torque on the upper rod.

The distance of the center of gravity from the point of suspension = L/2 - L/3  = L/6

Now, from moment equation

W1X2L/3 + 0.5XL/6 -T1XL/3 = 0

W1 = 1.525 N

Now, the tension in the upper equation

T2 = W1 + W + T1 = 1.525 + 0.5 + 3.3 = 5.325 N (it follows from the fact that net force = 0)

Posted Date: 2/26/2012 11:07:03 PM | Location : United States







Related Discussions:- What is the tension in the upper string, physics, Assignment Help, Ask Question on What is the tension in the upper string, physics, Get Answer, Expert's Help, What is the tension in the upper string, physics Discussions

Write discussion on What is the tension in the upper string, physics
Your posts are moderated
Related Questions
Short-Term Credit Decision In no more than one typed page, provide a statement of your decision to lend or not lend to this company based on your interpretation of the company

Transition towards IFRS Over the last few years, there has been a tremendous change in the world's capital markets. There has thus been a shift away from the local financial re

Maria runs a small business out of her home. She has expenses of $2,000 per year and uses the cash basis method of accounting. Her only employee is her cousin who works for her pa

how do I answer: with the aid of a decision tree prepare a quantitative report advising the company on the optimal course of action. (use a time horizon of 6years and ignore the ti

summarize chapter 2 in three pages, material costing and control

A boat is heading across a river at a velocity of 25 mph. The river is flowing downstream at 10 mph. What is the actual velocity of the boat?


Allocation surrounding to accounts An aspect of a lump-sum appropriation that is specific for expenses by particular government models and/or for particular requirements, actions,

The average cost per night of a hotel room in New York City is $273 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard

The waiting time for an incoming call at the front desk of mathematics Department follows an exponential distribution. During business hours, the average of the waiting times is 10