- If Cable Ab Is Subjected To A Tension Of 700n
- If Cable Ab Is Subjected To A Tension Of 700 Calorie
- If Cable Ab Is Subjected To A Tension Of 700
- If Cable Ab Is Subjected To A Tension Of 700r4
- If Cable Ab Is Subjected To A Tension Of 7000
If cable AB is subjected to a tension of 700 N, determine the tension in cables AC and AD and the magnitude of the vertical force F.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.Solution:
If cable AB is subjected to a tension of 700 N, determine the tension in cables AC and AD and the magnitude of the vertical force F. GEEN 2311-Statics and Dynamics of Rigid Bodies I Summer 2019 Instructor: Dr. Muhammad Azhar Ali Khan Submission Deadline: 1 st July 2019 4. 00fm.qxd 9/29/08 8:49 pm page an instructor’s solutions manual to accompany isbn-13: 978-0-495-24458-5 isbn-10: 0-495-24458-9 95 244585 00fm.qxd 9/29/. A transmission tower is supported by three cables as shown. The tension in cable BF is 700 lb. Determine (a) the moment of the force exerted by the cable BF ar B about the base point A, and (b) the perpendicular distance from point A to cable BF. AB AB PROBLEM 2.123 A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P = Pi and Q are applied to the ring to maintain the container in the position shown. Knowmg that W = 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable.
This question involves expressing forces in Cartesian vector form. If you are unsure on how to do this, read the detailed guide on expressing forces in Cartesian notation.We will first express each force along the ropes in Cartesian form. To do so, we will follow the following steps:
- Find the position vector for each rope
- Find the magnitude of each position vector
- Find the unit vector of each position vector
- Multiply the unit vector by the magnitude of the force in each cable
Locations of each point:
A:(0i+0j+6k)B:(2i+3j+0k)
C:(-1.5i+2j+0k)
D:(-3i-6j+0k)
The position vectors are:
We will now find the magnitude of each position vector:
magnitude of r_{AB},=,sqrt{(2)^2+(3)^2+(-6)^2},=,7 mmagnitude of r_{AC},=,sqrt{(-1.5)^2+(2)^2+(-6)^2},=,6.5 m
magnitude of r_{AD},=,sqrt{(-3)^2+(-6)^2+(-6)^2},=,9 m
The magnitude is equal to the square root of the sum of the squares of the vector. If the position vector was r,=,ai+bj+ck, then the magnitude would be, ![If cable ab is subjected to a tension of 700r4 If cable ab is subjected to a tension of 700r4](/uploads/1/1/8/7/118795653/803111206.png)
Next, we will find the unit vectors.
u_{AB},=,left(dfrac{2}{7}i+dfrac{3}{7}j-dfrac{6}{7}kright)u_{AC},=,left(-dfrac{1.5}{6.5}i+dfrac{2}{6.5}j-dfrac{6}{6.5}kright)
u_{AD},=,left(-dfrac{3}{9}i-dfrac{6}{9}j-dfrac{6}{9}kright)
The unit vector is each corresponding unit of the position vector divided by the magnitude of the position vector. If the position vector was r,=,ai+bj+ck, then unit vector, u,=,dfrac{a}{sqrt{(a^2)+(b^2)+(c^2)}}+dfrac{b}{sqrt{(a^2)+(b^2)+(c^2)}}+dfrac{c}{sqrt{(a^2)+(b^2)+(c^2)}}
We can now write each force in Cartesian vector form.
If Cable Ab Is Subjected To A Tension Of 700n
F_{AB},=,700left(dfrac{2}{7}i+dfrac{3}{7}j-dfrac{6}{7}kright)F_{AB},=left{200i+300j-600kright} N
We can now write our equation of equilibrium. All the forces added together must equal zero because the system is in equilibrium.
sum text{F},=,0F_{AB}+F_{AC}+F_{AD}+F,=,0
Since all forces added together must equal zero, that means each of the components ( x, y, z-components) added individually must add up to zero as well.
x-components:y-components:
Solving all three equations simultaneously gives us: