In the figure, a chain consisting of five links, each of mass 0.132 kg, is lifted vertically with a constant acceleration of magnitude a = 1.90 m/s2. Find the magnitudes of (a) the force on link 1 from link 2, (b) the force on link 2 from link 3, (c) the force on link 3 from link 4, and (d) the force on link 4 from link 5. Then find the magnitudes of (e) the force on the top link from the person lifting the chain and (f) the net force accelerating each link.
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This must be done in Newtons defined as kg-m/s^2. Kilograms are actually units of mass while Newtons are units of weight. The are obtained by multiplying the kilograms by g. In this case you have:
.132 kg x 9.81 m/s^2 = 1.29492 kg-m/s^2 aka Newtons.
Since the chain is being accelerated vertically at 1.90 m/s^2 we can obtain its additional "weight" or force by:
.132 kg x 1.90 m/s^2 = .2508 N; This is the force on the chain caused by acceleration, i.e., (e)
1.29492 + .2508 = 1.54572 N; This is the total force on the chain.
Since there are 5 links
a) 4/5 x 1.54572 = 1.236576 N
b) 3/5 x 1.54572 = .927432 N
c) 2/5 x 1.54572 = .618288 N
d) 1/5 x 1.54572 = .309144 N
I am not sure I understand question (f), each link would imply that they want the force on each link individually, i.e. (d). They might want the force on each link caused by lifting the chain which would be: 1/5 x .2508 N = .05016. This, however, would be technically wrong because gravity is also an acceleration.
I have a problem in that I can't see the figure so I don't know whether the first link is labeled at the top or bottom. I have assumed the first link is at the top because the problem doesn't make any sense otherwise.
.132 kg x 9.81 m/s^2 = 1.29492 kg-m/s^2 aka Newtons.
Since the chain is being accelerated vertically at 1.90 m/s^2 we can obtain its additional "weight" or force by:
.132 kg x 1.90 m/s^2 = .2508 N; This is the force on the chain caused by acceleration, i.e., (e)
1.29492 + .2508 = 1.54572 N; This is the total force on the chain.
Since there are 5 links
a) 4/5 x 1.54572 = 1.236576 N
b) 3/5 x 1.54572 = .927432 N
c) 2/5 x 1.54572 = .618288 N
d) 1/5 x 1.54572 = .309144 N
I am not sure I understand question (f), each link would imply that they want the force on each link individually, i.e. (d). They might want the force on each link caused by lifting the chain which would be: 1/5 x .2508 N = .05016. This, however, would be technically wrong because gravity is also an acceleration.
I have a problem in that I can't see the figure so I don't know whether the first link is labeled at the top or bottom. I have assumed the first link is at the top because the problem doesn't make any sense otherwise.