Tension on a Massive Rope: How to Calculate Tension at Different Points

In summary: Is the tension really ##68N##?In summary, a system consisting of a wide rope and two blocks of equal mass was lifted by an applied force of 9.0 N. The acceleration of the system was found to be 60 m/s^2. The tension at the top of the rope was calculated to be 68 N, which seems to be too high considering the force applied. Taking gravity into account, the tension may need to be recalculated.
  • #1
SakuRERE
68
5

Homework Statement


A system, consisting of a wide rope of mass 0.10 kg between two blocks each of mass 0.10 kg, is lifted by an applied force F = 9.0 N (Fig. 4 below). (a) Find the acceleration of the system. Find the tension at (b) the top of the rope, and (c) the bottom of one-fifth of the rope. Take g = 10 m/s2.
upload_2018-10-14_19-22-19.png

Homework Equations


Fnet=ma

The Attempt at a Solution


a) Fnet=ma
F- 3mg = ma
9- 3(0.1)(10) = 0.1a
6=0.1 a
a= 60 m/s^2

b) T- 2mg = ma
T-2(0.10)(10) = 0.10(60) (it's right to use the mass of rope by acceleration right?)
T-2=66
Ttop= 68N
is it right?

c) T- (4/5x m)- 10xm= (4/5)m x a
T- 0.08(10) - (0.10)(10)= 0.08(60) is this equation right
i don't if i got (the bottom of one-fifth of the rope) correctly or not. i considered the tension to equal to that part of the rope below 1/5 from the mass so that m of rope now is 4/5m
and also i have the lower mass (m). so is it right??
 

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  • #2
SakuRERE said:
a) Fnet=ma
F- 3mg = ma
9- 3(0.1)(10) = 0.1a
6=0.1 a
a= 60 m/s^2

Doesn't that seem a bit high to you?

SakuRERE said:
b) T- 2mg = ma
T-2(0.10)(10) = 0.10(60) (it's right to use the mass of rope by acceleration right?)
T-2=66
Ttop= 68N
is it right?

You have a ##9N## force and a tension of ##68N## Does that makes sense?
 
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  • #3
PeroK said:
Doesn't that seem a bit high to you?
You have a ##9N## force and a tension of ##68N## Does that makes sense?
it does, that's why I am asking here. i get number that are too big
 
  • #4
SakuRERE said:
it does, that's why I am asking here. i get number that are too big

What is the mass of your system?

What is the net external force on your system?

What is the acceleration of your system?
 
  • #5
PeroK said:
What is the mass of your system?
the total mass is 3(0.10) the two blocks and the rope
fnet is 9N
the acceleration... do you mean it should be F- 3(mg)=3ma?
 
  • #6
SakuRERE said:
the total mass is 3(0.10) the two blocks and the rope

If you mean: The total mass is ##0.3kg##, then yes.

SakuRERE said:
fnet is 9N

What about gravity?

SakuRERE said:
the acceleration... do you mean it should be F- 3(mg)=3ma?

I didn't mean anything. I just asked a question!
 
  • #7
PeroK said:
What about gravity?
the gravity force is down and each mass including the rope will have a weight downward.
PeroK said:
I didn't mean anything. I just asked a question!
Oh yeah, i am just trying to reach the solution fast :)
 
  • #8
SakuRERE said:
the gravity force is down and each mass including the rope will have a weight downward.

Exactly, so you need to take gravity into account when calculating the external force on your system.
 
  • #9
i JUst checked again my solution and i must have put 3m in a)
F-3mg= (3M)a
right? so a=20

and regarding the b) it would be
T-2mg=2ma
right?

and for c)
it would be
T-(1/5x0.10)g - 0.10g = (1/5x0.10+ 0.10) (20)
right?
 
  • #10
SakuRERE said:
i JUst checked again my solution and i must have put 3m in a)
F-3mg= (3M)a
right? so a=20

20 what? Units are important.

SakuRERE said:
and regarding the b) it would be
T-2mg=2ma
right?

That's the idea. It's called Newton's 2nd Law!
 
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  • #11
PeroK said:
20 what? Units are important.
a= 20 m/s^2

so it's right and i am done with it right?
 
  • #12
SakuRERE said:
a= 20 m/s^2

so it's right and i am done with it right?

You just have to calcuate the tension.
 
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Related to Tension on a Massive Rope: How to Calculate Tension at Different Points

1. What is tension on a massive rope?

Tension on a massive rope is the force that is applied to the rope in order to maintain its shape and structure. It is the force that is transmitted through the rope from one end to the other.

2. How is tension calculated on a massive rope?

Tension on a massive rope can be calculated using the formula T = mg, where T is the tension in newtons, m is the mass of the rope in kilograms, and g is the acceleration due to gravity (9.8 m/s^2).

3. What factors affect tension on a massive rope?

The tension on a massive rope is affected by the weight of the rope, the force applied to the rope, and the angle at which the force is applied. Other factors such as friction, elasticity of the rope, and external forces can also affect tension.

4. How does tension change in a massive rope under different conditions?

Tension on a massive rope can change depending on the amount of force applied to the rope, the direction and angle of the force, and the weight of the rope. It can also change if there are external forces acting on the rope, such as wind or other objects pulling on it.

5. Why is understanding tension on a massive rope important?

Understanding tension on a massive rope is important in various fields of science and engineering, such as in the construction of bridges, cranes, and other structures that use ropes for support. It also helps in analyzing the stability and safety of these structures. Additionally, understanding tension can also aid in the study of forces and motion.

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