If a force of 50N stretches a wire from 20m to 20.01m, what is the amount of for...
Question
If a force of 50N stretches a wire from 20m to 20.01m, what is the amount of force required to stretch the same material from 20m to 20.05m?Options
A) 250N
B) 200N
C) 100N
D) 50N
Related Lesson: Development of Force Concept | Force and Newton's Laws of Motion
The correct answer is A.
Explanation:
Original length = 20m
first new length = 20.01m
first new length = 20.01m
first increase in length = 20.01m - 20m = 0.01m
Second new length = 20.05m
second increase in length = 20.05 - 20m = 0.05m
From hooke's law = \( \frac{F_1}{e_1} = \frac{F_2}{e_2} \implies \frac{50}{0.01} = \frac{F_2}{0.05} \\
\implies F_2 = \frac{50 \times 0.05}{0.01} = 250N \)
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Original length = 20m
first new length = 20.01m
first increase in length = 20.01m - 20m = 0.01m
Second new length = 20.05m
second increase in length = 20.05 - 20m = 0.05m
From hooke's law = \( \frac{F_1}{e_1} = \frac{F_2}{e_2} \implies \frac{50}{0.01} = \frac{F_2}{0.05} \\
\implies F_2 = \frac{50 \times 0.05}{0.01} = 250N \)