Three kids A, B and C are pulling a rope as shown in the figure. What are the magnitudes of force with which B and C must pull in order to keep this system in equilibrium?
Answers
The magnitudes of force that B and C must pull is 17.32N and 10N respectively.
Given:
Force applied by A = 20N
To find:
Force applied by B and C
Solution:
Force is a vector quantity, therefore A, B and C are three vectors.
Therefore,
Components of Vector A = x and y
x component = 20 cos30°
= 20√3/2
= 17.32N
y component
= 20 sin30°
= 20 *1/2
= 10N
For the system to be in equilibrium, forces B and C should be equal and opposite to components of force A.
Magnitude of Force B, |B| = x component = 17.32N
Magnitude of Force C, |C| = y component = 10N
Resultant of force B and C should be equal to force |A|= 20N, to cancel out the effect of force A.
Now,
According to Law of Parallelogram, resultant of two perpendicular vectors is:
R= √ (B² + C²)
R= √ (17.32² + 10²)
= 20N = Magnitude of Force A
Answer: The magnitudes of force that B and C must pull is 17.32N and 10N respectively.
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