The ball D has a mass of 20 kg. If a force of F = 100 N is applied horizontally to the ring at A, determine the largest dimension d the force in cable AC is zero.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.
Solution:
Show me the final answer↓ Let us draw a free body diagram around ring A as follows:
(Note that cable AC is not shown in the free body diagram because the force in the cable is zero.)
EQUATIONS OF EQUILIBRIUM (Section 5.6) As stated earlier, when a body is in equilibrium, the net force and the net moment equal zero, i.e., F = 0 and MO = 0. The collar has a mass of 20 k g and slides along the smooth rod. Two springs are attached to it and the ends of the rod as shown. If each spring has an uncompressed length of 1 m and the collar has a speed of 2 m / s when s = 0, determine the maximum compression of each spring due to the back-and-forth (oscillating) motion of the collar.
A sled with a mass of 20 kg slides along frictionless ice at 4.5 m/s. It then crosses a rough patch of snow which exerts a friction force of 12N. How far does it slide on the snow before coming to rest? The crate, which has a mass of 100 kg, is subjected to the action of the two forces. If it is originally at rest, determine the distance it slides in order to attain a speed of The coefficient of kinetic friction between the crate and the surface is m k = 0.2.
dfrac{text{sin}theta}{text{cos}theta},=,1.962 (remember that dfrac{text{sin}theta}{text{cos}theta},=,text{tan}theta)
text{tan}theta,=,1.962 (solve for theta)
theta,=,text{tan}^{-1}(1.962) theta,=,63^0
To figure out d, we can use trigonometry. We can write the following:
text{tan},(63^0),=,dfrac{(1.5,+,d)}{2}
(If you are unclear about this step, remember that text{tan}theta,=,dfrac{text{opposite}}{text{adjacent}}. Refer to the diagram again to see how we got the values for opposite and adjacent.)
The Collar Has A Mass Of 20kg And Rests On The Smooth Rod
(solve for d)
d,=,2.42 m
If, you wanted, you can also figure out F_{AB} by substituting the value of theta we found back into eq.1.F_{AB},=,dfrac{100}{text{cos},(63^0)}
F_{AB},=,220 N
Final Answer:
d,=,2.42 m
This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 3, question 3-42.