Answer
(a) $T = 10.78~m$, (where $m$ is the mass of the truck)
Note that $T = 1.10~mg$
(b) $T = 10.78~m$, (where $m$ is the mass of the truck)
Note that $T = 1.10~mg$
Work Step by Step
(a) If the downward speed of the truck is decreasing at a rate of $0.10~g$, then the upward acceleration is $0.10~g$. We can find the tension in the cable:
$\sum F = ma$
$T-mg = ma$
$T = m~(a+g)$
$T = m~(0.10~g+g)$
$T = m~(1.10~g)$
$T = m~(1.10)(9.80)$
$T = 10.78~m$, (where $m$ is the mass of the truck)
Note that $T = 1.10~mg$
(b) If the downward speed of the truck is decreasing at a rate of $0.10~g$, then the upward acceleration is $0.10~g$. We can find the tension in the cable:
$\sum F = ma$
$T-mg = ma$
$T = m~(a+g)$
$T = m~(0.10~g+g)$
$T = m~(1.10~g)$
$T = m~(1.10)(9.80)$
$T = 10.78~m$, (where $m$ is the mass of the truck)
Note that $T = 1.10~mg$
