A 10-lb collar is attached to a spring and slides without friction along a fixed
ID: 3163085 • Letter: A
Question
A 10-lb collar is attached to a spring and slides without friction along a fixed rod in a vertical plane. The spring has an undeformed length of 14 in. and a constant k = 18 lb/in. Knowing that the collar is released from rest in the position shown, determine the force exerted by the rod on the collar at (a) Point A, (b) Point B. Both these points are on the curved portion of the rod. (Round the final answer to one decimal place.) The force exerted by the rod on the collar at Point A is The force exerted by the rod on the collar at Point BExplanation / Answer
a)
length of spring , x = sqrt(14^2 + 14^2) = 19.80 in
force = kx = 18 * (19.80 - 14) = 104.4 lb
force by spring = 104.40 lb = 104.40cos45i + 104.40sin45j
mv^2/2 = k * (28^2 + 14^2 - 14^2 - 14^2) / 2
mv^2/2 = 18 *294
mv^2 = 10584
centrifugal force = mv^2/r = 10584/14 = 756 lb
net = 756i + 104.40cos45i + 104.40sin45j
net = 756i + 73.81 i + 73.82 j
net = 829.81 i + 73.82 j
|Fnet| = sqrt(829.81^2 + 73.82^2 )
|Fnet| = 833.08 lb
b) force = 18* (28 - 14) = 252 lb
force by spring = 252 j lb
mv^2/2 = k * (28^2 + 14^2 - 14^2 - 14^2) / 2
mv^2/2 = 18 *294
mv^2 = 10584
centrifugal force = mv^2/r = 10584/14 = 756 lb
net = 756 i +252 j lb
|Fnet| = sqrt(756^2 + 252^2 )
|Fnet| = 797 lb
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