What Is the Tension in the Rope When a Railroad Car Accelerates?

  • Thread starter Thread starter litz057
  • Start date Start date
  • Tags Tags
    Car
Click For Summary

Homework Help Overview

The problem involves a 7.1 kg object hanging from a rope attached to a railroad car that accelerates, causing the rope to form an angle of 7.7 degrees with the vertical. Participants are tasked with determining the tension in the rope while considering the forces acting on the object.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between the tension in the rope and the forces acting on the object, including gravitational force and the acceleration of the railroad car. There are attempts to apply trigonometric relationships and Newton's second law to find the tension.

Discussion Status

Some participants have provided guidance on considering both gravitational and horizontal accelerations, suggesting the use of vector sums. Others have raised questions about the understanding of trigonometry and free body diagrams, indicating a lack of consensus on the approach to take.

Contextual Notes

There is mention of confusion regarding terminology used by a professor, as well as varying levels of understanding of basic trigonometry and vector concepts among participants. Some participants express frustration with the complexity of the problem and the need for foundational knowledge to proceed.

litz057
Messages
35
Reaction score
1

Homework Statement


A 7.1 kg object hangs at one end of a rope that is attached to a support on a railroad car. When the car accelerates to the right, the rope makes an angle of 7.7 degrees with the vertical, as shown in the figure below. What is the tension in the rope in Newtons?

Homework Equations


Ft/Fg=ma/mg=ag

The Attempt at a Solution


Ft/Fg=ma/mg=ag
tan(7.7)=a/9.81
tan(7.7)*9.81=a
1.326364039 m/s^2 = a
Railroad Car.gif
 
Physics news on Phys.org
You've done the hard part. What's your question?
 
  • Like
Likes   Reactions: litz057
Bystander said:
You've done the hard part. What's your question?
How do I find the correct answer? I submitted the answer that I posted above, but it was marked incorrect. Is there a step that I am missing?
 
They asked for the tension in the rope, not the acceleration of the mass.

Chet
 
  • Like
Likes   Reactions: litz057
Chestermiller said:
They asked for the tension in the rope, not the acceleration of the mass.

Chet
How do I use the acceleration to find the tension in the rope? I tried using F=ma
F=ma
F=7.1* 1.3264
F= 9.4172 N
This is not the correct answer. How do I find the tension from the acceleration?
 
You have two accelerations, gravitational, and of the railroad car. Can you do the vector sum of those two?
 
  • Like
Likes   Reactions: litz057
If the tension in the rope is F, how is Ft related to F? How is Fg related to F?

Chet
 
  • Like
Likes   Reactions: litz057
Bystander said:
You have two accelerations, gravitational, and of the railroad car. Can you do the vector sum of those two?
I am not completely sure how to do the vector sum. Do I just add 9.81 and 1.3264?
 
Chestermiller said:
If the tension in the rope is F, how is Ft related to F? How is Fg related to F?

Chet
Ft is the force relative to the train and Fg is the force relative to the ground.
 
  • #10
litz057 said:
Ft is the force relative to the train and Fg is the force relative to the ground.
Algebraically, if the tension in the rope is F, and θ is the angle that the rope makes with the vertical, how is Ft related to F? How is Fg related to F?
 
  • #11
Chestermiller said:
Algebraically, if the tension in the rope is F, and θ is the angle that the rope makes with the vertical, how is Ft related to F? How is Fg related to F?
Does F=tan(Fg/Ft)?
 
  • #12
litz057 said:
Does F=tan(Fg/Ft)?
No. Where did you get the equation Ft/Fg=ma/mg from, and what does it mean to you? Have you had trigonometry yet? Have you learned about vectors yet? If so, if you know two perpendicular components of a vector, how do you find the magnitude of the vector?

Chet
 
  • #13
Chestermiller said:
No. Where did you get the equation Ft/Fg=ma/mg from, and what does it mean to you? Have you had trigonometry yet? Have you learned about vectors yet? If so, if you know two perpendicular components of a vector, how do you find the magnitude of the vector?

Chet
The equation was given to me by a classmate. It means that the force (acceleration) relative to the train divided by the force relative to the ground equals (the mass of the object times the force relative to the train) divided by (the mass of the object times the gravitational force). I have not had trigonometry for a few years.

Ft/Fg=ma/mg
(1.326364039/9.81)=((7.1)(1.326364039))/((7.1)(9.81))?
 
  • #14
litz057 said:
The equation was given to me by a classmate. It means that the force (acceleration) relative to the train divided by the force relative to the ground equals (the mass of the object times the force relative to the train) divided by (the mass of the object times the gravitational force). I have not had trigonometry for a few years.

Ft/Fg=ma/mg
(1.326364039/9.81)=((7.1)(1.326364039))/((7.1)(9.81))?
None of this makes any sense to me. It sounds like metaphysics rather than physics. What about you, Bystander?

litz057, what would you have done if your friend wasn't there to help you? Then, you could not even have determined the horizontal acceleration (or as you incorrectly call it, the acceleration relative to the train).

Have you drawn a free body diagram showing the forces acting on the mass? If you don't know the most basic trig and you don't know anything about vectors, you are not going to be able to solve this problem, and we are not going to be able to help you. So, my advise is to learn basic trig, learn vectors, and learn how to apply free body diagrams to write down a force balance on an object.

Chet
 
  • #15
Chestermiller said:
None of this makes any sense to me. It sounds like metaphysics rather than physics. What about you, Bystander?

litz057, what would you have done if your friend wasn't there to help you? Then, you could not even have determined the horizontal acceleration (or as you incorrectly call it, the acceleration relative to the train).

Have you drawn a free body diagram showing the forces acting on the mass? If you don't know the most basic trig and you don't know anything about vectors, you are not going to be able to solve this problem, and we are not going to be able to help you. So, my advise is to learn basic trig, learn vectors, and learn how to apply free body diagrams to write down a force balance on an object.

Chet
I have similar equations. I had an similar equation T=ma/mg, among a plethora of other equations (relevant or not). In these types of problems, my professor calls the horizontal acceleration the acceleration relative to the train. I know basic trig and basic trig functions. Vectors is an amount that involves a magnitude and direction.
 
  • #16
litz057 said:
I have similar equations. I had an similar equation T=ma/mg, among a plethora of other equations (relevant or not). In these types of problems, my professor calls the horizontal acceleration the acceleration relative to the train.
I have trouble believing that a professor of physics could use such incorrect terminology.
I know basic trig and basic trig functions. Vectors is an amount that involves a magnitude and direction.
I'm going to have to withdraw from this this thread. I don't feel that I can help you until you have more knowledge of vectors, and are able to draw proper free body diagrams, identify the forces in these diagrams, and write down the relevant force balance equations. Sorry.

Chet
 

Similar threads

What is the tension in a rope when a monkey accelerates up?
  • · Replies 66 ·
3
Replies
66
Views
7K
Monkey accelerating up and down a rope
  • · Replies 38 ·
2
Replies
38
Views
5K
Two masses connected by a weighted rope pulled vertically
  • · Replies 5 ·
Replies
5
Views
5K
Problem with pulleys - two fixed and one movable
  • · Replies 22 ·
Replies
22
Views
2K
Tension in Ropes: Solving Forces on Trunk
  • · Replies 7 ·
Replies
7
Views
5K
Object hangs from rope on a railroad car
  • · Replies 10 ·
Replies
10
Views
7K
Need help with a pulley and tension problem
  • · Replies 3 ·
Replies
3
Views
2K
Tension on a Massive Rope: How to Calculate Tension at Different Points
  • · Replies 11 ·
Replies
11
Views
3K
Find the Tension in the cable when the lift is moving at constant speed
  • · Replies 3 ·
Replies
3
Views
2K
Calculating tensions in ropes suspending an onject
  • · Replies 2 ·
Replies
2
Views
2K