When a spring is only pulled by Bob with 200 N force, the spring stretches 20 cm. If the same spring is pulled by Bob and Carlos with 200 N forces each, the string will stretch 40 cm.
The elasticity is followed the Hooke's Law:
F = kx
Where:
F = force applied
k = spring constant
x = length of extension / compression
From the Hooke's Law, we know that the applied force is directly proportional to the change of length, or
F2 : F1 = x2 : x1
Parameters given in the problem:
F1 = 200 N (Force applied by Bob)
x1 = 20 cm
F2 = 200 + 200 = 400 N (Forces applied aby Bob and Carlos)
Therefore,
400 : 200 = x2 : 20
x2 = 400 x 20 / 200 = 40 cm
Thus, when both Bob and Carlos pulls the spring, the spring will stretch 40 cm
Complete question:
The left end of a spring is attached to a wall. When Bob pulls on the right end with a 200 N force, he stretches the spring by 20 cm . The same spring is then used for a tug-of-war between Bob and Carlos. Each pulls on his end of the spring with a 200 N force.
How far does the spring stretch?
Learn more about Hooke's Law here
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