Two blocks each of mass m = 3.30 kg are fastened to the top of an elevator as in the figure below.
(a) If the elevator accelerates upward at 1.6 m/s2, find the tensions T1 and T2 in the upper and lower strings.
T1_______ N
T2________N
figure: http://www.webassign.net/sercp8/p4-21a.gif
(a) If the elevator accelerates upward at 1.6 m/s2, find the tensions T1 and T2 in the upper and lower strings.
T1_______ N
T2________N
figure: http://www.webassign.net/sercp8/p4-21a.gif
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The upper string supports the weight of both masses plus provides additional force to accelerate them upward. The lower string does the same but for the lower mass only
T1 = (m1 + m2) (g + a) = (6.6) ( 9.8 + 1.6) = 75.2 N
T2 = half of T1 = 37.6 N
T1 = (m1 + m2) (g + a) = (6.6) ( 9.8 + 1.6) = 75.2 N
T2 = half of T1 = 37.6 N
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we will write newton's second laws for each of the masses, I will call the upper mass 1 and the lower mass 2
the forceson the lower mass are the tension in string 2 acting up, the weight down, and these must combine to produce an ma term where a=1.6m/s/s
so we have
T2-m2g = m2a = 1.6m2
for the upper mass T1 pulls up, T2 and m1 g act down:
T1 - m1g - T2= 1.6m1
from the first equation we know that T2=m2(g+1.6)
sub into the T1 equation:
T1- m1g -m2(g+1.6)=1.6m1
you know m1 =m2=3.3, g=9.8, solve for T1, then for T2
the forceson the lower mass are the tension in string 2 acting up, the weight down, and these must combine to produce an ma term where a=1.6m/s/s
so we have
T2-m2g = m2a = 1.6m2
for the upper mass T1 pulls up, T2 and m1 g act down:
T1 - m1g - T2= 1.6m1
from the first equation we know that T2=m2(g+1.6)
sub into the T1 equation:
T1- m1g -m2(g+1.6)=1.6m1
you know m1 =m2=3.3, g=9.8, solve for T1, then for T2