A light spring has a force-length relationship as shown in the figure below. Wha
ID: 1419023 • Letter: A
Question
A light spring has a force-length relationship as shown in the figure below. What is the spring constant? How much work is necessary to change the length of the spring from 0.75 m, to 1.0 m? This spring is now placed or a horizontal frictionless surface as shown below. One end is fixed and can pivot about the point A, the other end has a mass of 2.0 kg attached to it. The mass is set moving at constant speed in a circle of radius 1.0 m which is the same as the length of the spring. What is the speed of the mass?Explanation / Answer
The relationship between the force and length for a spring is
F = - k x
Where x is the length and k is the spring constant
The spring constant k = F / x
spring constant is the slope of the force - length graph
k = slope = (50 - 25) /(1 - 0.75) = 100 N /m
b) The work done is
W = (1/2) k xi2 - (1/2) k xf2
Where the subscripts i and f for the length x refers initial and final
W = (1/2) 100 x 0.752 - (1/2) x 100 x 12 = 28.125 - 50 = -21.875 J
c) The centripetal force is provided by the spring force
m v2 / x = k x
Where v is the velocity of the rotation , x is the radius of the circular motion , m is the mass
v = sqrt (k x2 /m )
v = sqrt (100 x 12 / 2)
v = 7.071 m/s
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.