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A ball of mass 620 g hangs from a spring whose stiffness is 175 newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless, as shown in the figure. In this situation the spring is stretched, and its length is 15 cm. What would be the relaxed length of the spring, if it were detached from the ball and laid on a table?
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Spring being pulled to the right of the normal with a distance of 8cm. Using simple trigonometry I found that the angle between the spring and the normal was 32.231 degrees if that helps.

Draw a force vector diagram for the system in equilibrium (right-angle triangle) ..
T = tension in spring (hypotenuse) .. directed towards anchor point
Weight (mg) .. vertical component of T (upwards)
String force .. horiz. component of T (to right)

Cos32.2 = mg / T
T = mg/cos32.2 .. .. (0.62kg x 9.80)/cos32.2 .. .. T =7.18 N

Spring constant .. k = F/e
e = F/k .. .. 7.18N / 175N/m .. .. e = 0.0410 m = 4.10cm

Natural length of spring .. Lo = (15.0 - 4.10)cm .. .. .. ?Lo = 10.9cm
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