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
Answers
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:
[tex]\sum F=0[/tex]
T-W=0
T=W
T=mg
[tex]T=(56kg)(9.81m/s^{2})[/tex]
T=549.36N upwards
b)
For part b, since the object is accelerating downwards, we wil say that it's acceleration is negative, so [tex]a=-1.8m/s^{2}[/tex]
so we can do a sum of forces again:
[tex]\sum F=ma[/tex]
so
T-W=ma
T=ma +W
T=ma+mg
T=m(a+g)
and now we substitute:
[tex]T=(56kg)(-1.8 m/s^{2}+9.81 m/s^{2})[/tex]
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 [tex]a =1.8m/s^{2}[/tex]
we can take the solved equation we got on the previous part of the problem, so we get:
T=m(a+g)
[tex]T =(56kg)(1.8 m/s^{2}+9.81 m/s^{2})[/tex]
which yields:
T=650.16N upwards
The tension force in the rope when the object moves upward at a constant velocity is 548.8 N.
The tension force in the rope when the object accelerates downward at a constant acceleration is 448 N.
The tension force in the rope when the object accelerates upward at a constant acceleration is 649.6 N.
The given parameters:
Mass of the object, m = 56 kgThe tension force in the rope when the object moves upward at a constant velocity;
T = ma + mg
at constant velocity, a = 0
T = mg
T = 56(9.8)
T = 548.8 N
The tension force in the rope when the object accelerates downward at a constant acceleration of 1.8 m/s².
T = mg - ma
T = m(g - a)
T = 56(9.8 - 1.8)
T = 448 N
The tension force in the rope when the object accelerates upward at a constant acceleration of 1.8 m/s².
T = mg + ma
T = m(g + a)
T = 56(9.8 + 1.8)
T = 649.6 N
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Answers
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Answers
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