Question

A 56 kg object is attached to a rope, which can be used to move the load vertically.

Answer 1

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:

$\sum F=0$

T-W=0

T=W

T=mg

$T=(56kg)(9.81m/s^{2})$

T=549.36N upwards

b)

For part b, since the object is accelerating downwards, we wil say that it's acceleration is negative, so $a=-1.8m/s^{2}$

so we can do a sum of forces again:

$\sum F=ma$

so

T-W=ma

T=ma +W

T=ma+mg

T=m(a+g)

and now we substitute:

$T=(56kg)(-1.8 m/s^{2}+9.81 m/s^{2})$

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 $a =1.8m/s^{2}$

we can take the solved equation we got on the previous part of the problem, so we get:

T=m(a+g)

$T =(56kg)(1.8 m/s^{2}+9.81 m/s^{2})$

which yields:

T=650.16N upwards