Mass hanging in a boxcar accelerating

In summary, the question asks for the approximate tension in a rope in a train with a mass of 1 kg and an acceleration of 7 m/s^2. The correct answer is 12 N, but the attempt at a solution yields a different answer due to a mistake in the calculation of the x-component. The correct calculation should be 1*7=7 N.
  • #1
brake4country
216
7
1. Homework Statement
A mass of 1 kg hangs inside a boxcar of a train. If the train accelerates at 7 m/s^2, what is the approximate tension in the rope?

A: 12 N

Homework Equations


F=ma

The Attempt at a Solution


I originally thought of doing this problem as pythagorean theorem, but I wanted to work out the x and y components for practice. Breaking up the components:
ΣFy=may
Ty-mg = may
Ty=10N

ΣFx=max
Tx=10*7
Tx=70N

Thus, T2=102+702
T=71 N

The problem sets it up just like I do but get 12 N for their answer:
T2=ma2+mg2

What am I doing wrong? Thanks in advance!
 
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  • #2
brake4country said:
1. Homework Statement
A mass of 1 kg hangs inside a boxcar of a train. If the train accelerates at 7 m/s^2, what is the approximate tension in the rope?

A: 12 N

Homework Equations


F=ma

The Attempt at a Solution


I originally thought of doing this problem as pythagorean theorem, but I wanted to work out the x and y components for practice. Breaking up the components:
ΣFy=may
Ty-mg = may
Ty=10N

ΣFx=max
Tx=10*7
Tx=70N

Thus, T2=102+702
T=71 N

The problem sets it up just like I do but get 12 N for their answer:
T2=ma2+mg2

What am I doing wrong? Thanks in advance!
Can you show us your free body diagram for this problem? That is generally the first/best step on these problems. :smile:
 
  • #3
brake4country said:
Breaking up the components:
ΣFy=may
Ty-mg = may
Ty=10N

ΣFx=max
Tx=10*7 ⇐
Tx=70N
Check the mass value used for the calculation of the x-component.
 

FAQ: Mass hanging in a boxcar accelerating

What is mass hanging in a boxcar accelerating?

Mass hanging in a boxcar accelerating refers to the scenario where objects of varying masses are suspended from the ceiling of a boxcar that is accelerating. This situation is often used as a thought experiment to understand the effects of acceleration on objects with different masses.

How does the acceleration affect the objects?

The acceleration causes the objects to experience a force known as the "pseudo-force" or "fictitious force" that is proportional to their mass. This force acts in the opposite direction of the acceleration and causes the objects to appear to hang at an angle instead of straight down. The larger the mass, the greater the force experienced.

What happens when the boxcar reaches a constant velocity?

At a constant velocity, the acceleration becomes zero and the pseudo-force disappears. This results in the objects hanging vertically again, as if there was no acceleration present.

How does this relate to Newton's laws of motion?

This scenario is an example of Newton's first law of motion, also known as the law of inertia. The objects in the boxcar want to maintain their state of rest or motion, but the acceleration of the boxcar forces them to move in a different direction. It also demonstrates the concept of the pseudo-force, which is a result of acceleration and not a real physical force.

Can this scenario be applied to real-life situations?

Yes, this scenario can be applied to real-life situations, such as the feeling of being pushed back into your seat when a car accelerates or the sensation of weightlessness in space due to the absence of gravity. It also helps in understanding the forces acting on objects in moving vehicles, such as roller coasters or airplanes.

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