A 56 kg object is attached to a rope, which can be used to move the load vertically. a. What is the tension force in the rope when the object moves upward at a constant velocity?

b. What is the tension force in the rope when the object accelerates downward at a constant

acceleration of 1.8 m/s2

c. What is the tension force in the rope when the object accelerates upward at a constant

acceleration of 1.8 m/s2

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:

T-W=0

T=W

T=mg

T=549.36N upwards

b)

For part b, since the object is accelerating downwards, we wil say that it's acceleration is negative, so

so we can do a sum of forces again:

so

T-W=ma

T=ma +W

T=ma+mg

T=m(a+g)

and now we substitute:

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

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

T=m(a+g)

which yields:

T=650.16N upwards

wavelength divides in half and speed stays the same.