Answer:
a) T=549.36N Upwards
b) T=448.56N Upwards
c) T=650.16N Upwards
Explanation:
The very first thing we can do to solve this problem is to draw a free body diagram we can use to analyze the situation (see attached picture).
On the diagram we can see there are only two forces acting on the object: the tension of the rope and the weight of the object itself.
a)
Since the object is moving at a constant speed, this means that its acceleration will be zero. So we can do a sum of forces like this:
![\sum F=0](https://tex.z-dn.net/?f=%5Csum%20F%3D0)
T-W=0
T=W
T=mg
![T=(56kg)(9.81m/s^{2})](https://tex.z-dn.net/?f=T%3D%2856kg%29%289.81m%2Fs%5E%7B2%7D%29)
T=549.36N upwards
b)
For part b, since the object is accelerating downwards, we wil say that it's acceleration is negative, so ![a=-1.8m/s^{2}](https://tex.z-dn.net/?f=a%3D-1.8m%2Fs%5E%7B2%7D)
so we can do a sum of forces again:
![\sum F=ma](https://tex.z-dn.net/?f=%5Csum%20F%3Dma)
so
T-W=ma
T=ma +W
T=ma+mg
T=m(a+g)
and now we substitute:
![T=(56kg)(-1.8 m/s^{2}+9.81 m/s^{2})](https://tex.z-dn.net/?f=T%3D%2856kg%29%28-1.8%20m%2Fs%5E%7B2%7D%2B9.81%20m%2Fs%5E%7B2%7D%29)
which yields:
T=448.56N upwards (in this particular case, the tension always goes upwards)
c)
Since the object is moving upwards, we can say that its acceleration will be positive, so ![a =1.8m/s^{2}](https://tex.z-dn.net/?f=a%20%3D1.8m%2Fs%5E%7B2%7D)
we can take the solved equation we got on the previous part of the problem, so we get:
T=m(a+g)
![T =(56kg)(1.8 m/s^{2}+9.81 m/s^{2})](https://tex.z-dn.net/?f=T%20%3D%2856kg%29%281.8%20m%2Fs%5E%7B2%7D%2B9.81%20m%2Fs%5E%7B2%7D%29)
which yields:
T=650.16N upwards