1) Two blocks each of mass m = 2.98 kg are fastened to the top of an elevator as
ID: 1784395 • Letter: 1
Question
1) Two blocks each of mass m = 2.98 kg are fastened to the top of an elevator as in the figure. (a) If the elevator has an upward acceleration a = 1.60 m/s2, find the tensions Ti and T2 in the upper and lower strings. (b) If the strings can withstand a maximum tension of 91.0 N, what maximum acceleration can the elevator have before the upper string breaks? (show the steps of your calculation and indicate units to get credit) 2) A river has a steady speed of 0.600 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. (a) If the student can swim at a speed of 1.40 m/s in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? ur calculation and indicate units to get credit)Explanation / Answer
1)
for lower mass
T2 - mg - m*a
T2 = m*(g + a)
T2 = 2.98*(9.8+1.6)
T2 = 33.972 N
for upper mass
T1 - mg - T2 = m*a
T1 = ma + mg + T2
T1 = 67.944 N
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(b)
for lower
T2 - mg = m*a
T2 = mg + ma
for upper
T1 - mg - T2 = m*a
T1 = mg + ma + T2
T1 = mg + ma + mg + ma
T1 = 2*m*(g+a)
given T1 = 91 N
91 = 2*2.98*(9.8+a)
acceleration a = 5.47 m/s^2
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2)
(a)
speed of student relative to river v = sqrt(1.4^2-0.6^2) = 1.26 m/s
time taken to upstream = d/v = 1000/1.26 = 793.65 s
time taken to downstream = d/v = 1000/1.26 = 793.65 s
total time = 1587.3 s = 26.455 minutes
(b)
In still water speed v = 1.4 m/s
total time = 2d/v = 2*1000/1.4 = 1428.57 s = 23.8 minutes
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