If the chain is lowered at a constant speed v = 1.2 m/s, determine the normalreaction exerted on the floor as a function of time. The chain has a mass of 80kg and a total length of 6 m.a) (16t + 9.8) N vertically upwardb) (16t + 9.8) N vertically downwardc) (16t + 19.2) N vertically downwardd) (16t + 19.2) N vertically upward
Answers
Normal reaction exerted on the floor as a function of time is (16t + 19.2)N vertically downward
Explanation:
=> It is given that,
Mass of a chain = 80 kg
total length of a chain = 6 m
speed of the chain = 1.2 m/s
normal reaction exerted on the floor = ?
=> [As we know, linear density of the chain is equal to the mass divided by the length of the chain.]
Linear density = mass of the chain / length of the chain
= 80 / 6
= 13.33 kg/m
=> Weight of chain lying on ground:
W = mg = 13.33 * 1.2 t
= 15.99 t
≈ 16 t kg/s
=> According to Newton’s 2nd law of motion,
F=dP/dt
but p=mv
∴ F=d(mv)/dt
F= v dm/dt
= 1.2 * 1.6
= 19.2 N
=> Normal reaction exerted on the floor as a function of time:
N = W + F
= 16t + 19.2 N
The normal reaction exerted on the floor as a function of time is (16t + 19.2) N vertically downward.
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