# 2010 HSC question (1 Viewer)

#### ron13

##### New Member

a. Why does the mass hang with the string at an angle to the vertical? (2marks)
b. The string then breaks and the mass falls. Indicate the pass of the mass on the diagram above. Explain why the mass has taken this path. (3 marks)
<o></o>
What are the forces acting on the pendulum bob?

Also, what are fictitious forces?

#### k02033

##### Member
a. because the train is accelerating

b. it will be just be a regular projectile, with initial velocity given by the velocity of the train at the time the string is cut. This is because the only force acting on the mass is gravity.

Newton's Laws do not work in non inertial frames and things can appear to accelerate even when no net force is imposed. Fictitious forces are forces made up in attempt to compensate for this.

#### ohexploitable

##### hey
Fictitious forces or inertial forces are apparent forces which affect objects in a non-inertial frame of reference, in this case, there are inertial forces acting on the pendulum to make it hang at an angle.

#### ohexploitable

##### hey
b. it will be just be a regular projectile, with initial velocity given by the velocity of the train at the time the string is cut. This is because the only force acting on the mass is gravity.
But the train is accelerating, there will be inertial forces pushing the object to the right.

#### k02033

##### Member
I think the question is asked as if you are an observer outside of the train. Since that reference frame is inertial what I said holds.

Last edited:

#### s2 SEductive

##### MostDefinitelyIncredible
I think the question is asked as if you are an observer outside of the train. Since that reference frame is inertial what I said holds.
"A train is travelling on a straight horizontal track. A student on the train attaches a mass on a string to the ceiling of the train. The student observes that the mass remains stationary in the position shown."

#### k02033

##### Member
"A train is travelling on a straight horizontal track. A student on the train attaches a mass on a string to the ceiling of the train. The student observes that the mass remains stationary in the position shown."
Ok few more things i can point out to convince you that I am right.

Firstly the drawing given is clearly from a perspective of an observer outside, this is irrespective of what you wrote.

Only motion studied in HSC physics in any depth is projectile motion.

Try and draw the motion of the mass that experiences the fictitious force and gravity as seen by the observer in the train, see what happens.

#### nelsonzheng

##### New Member

amirite?
(might've exaggerated how far forward the ball goes)

#### k02033

##### Member

amirite?
(might've exaggerated how far forward the ball goes)
Suppose we are to draw it from the point of view of the observer inside the train, then he would observer an horizontally compacted version of a projectile motion. Now how compacted this motion is depends on the acceleration of the train. Since we are not given this information, doing this drawing is impossible. And even if the acceleration is given, one way to get an accurate drawing is to resolve vectors, perhaps rotate the axis to to align with the resultant force and solve some equations of motion in the new axis, clearly not expected of a HSC student.

If I were marking your drawing i would say:

First of all, your answer is not clear since you have not stated which reference frame you used.

If you were drawing it from the observer inside then your answer was just a blind guess and cant be right or wrong.

If you were drawing for the observer outside then you are right (the horizontal spacing should be equal)

Also what you wrote in brackets "(might've exaggerated how far forward the ball goes) " is wrong because we don't know the speed of the train when the string is cut, so you cant say you exaggerated, in fact you could be under exaggerating, we just dont know.

Sorry if i was too critical, little frustrated today...

Last edited:

#### s2 SEductive

##### MostDefinitelyIncredible
Suppose we are to draw it from the point of view of the observer inside the train, then he would observer an horizontally compacted version of a projectile motion. Now how compacted this motion is depends on the acceleration of the train. Since we are not given this information, doing this drawing is impossible. And even if the acceleration is given, one way to get an accurate drawing is to resolve vectors, perhaps rotate the axis to to align with the resultant force and solve some equations of motion in the new axis, clearly not expected of a HSC student.

If I were marking your drawing i would say:

First of all, your answer is not clear since you have not stated which reference frame you used.

If you were drawing it from the observer inside then your answer was just a blind guess and cant be right or wrong.

If you were drawing for the observer outside then you are right (the horizontal spacing should be equal)

Also what you wrote in brackets "(might've exaggerated how far forward the ball goes) " is wrong because we don't know the speed of the train when the string is cut, so you cant say you exaggerated, in fact you could be under exaggerating, we just dont know.

Sorry if i was too critical, little frustrated today...
Oh ok makes sense =]

#### nelsonzheng

##### New Member
Suppose we are to draw it from the point of view of the observer inside the train, then he would observer an horizontally compacted version of a projectile motion. Now how compacted this motion is depends on the acceleration of the train. Since we are not given this information, doing this drawing is impossible. And even if the acceleration is given, one way to get an accurate drawing is to resolve vectors, perhaps rotate the axis to to align with the resultant force and solve some equations of motion in the new axis, clearly not expected of a HSC student.

If I were marking your drawing i would say:

First of all, your answer is not clear since you have not stated which reference frame you used.

If you were drawing it from the observer inside then your answer was just a blind guess and cant be right or wrong.

If you were drawing for the observer outside then you are right (the horizontal spacing should be equal)

Also what you wrote in brackets "(might've exaggerated how far forward the ball goes) " is wrong because we don't know the speed of the train when the string is cut, so you cant say you exaggerated, in fact you could be under exaggerating, we just dont know.

Sorry if i was too critical, little frustrated today...
Thanks for clarifying. I was merely producing a graphic to help people understand.

#### Physics_FTW

##### New Member

amirite?
(might've exaggerated how far forward the ball goes)
The ball should go in the other direction.. As the mass is hanging to the right, this means that the train is accelerating to the left, therefore the ball should bounce to the right

#### Physics_FTW

##### New Member
Suppose we are to draw it from the point of view of the observer inside the train, then he would observer an horizontally compacted version of a projectile motion. Now how compacted this motion is depends on the acceleration of the train. Since we are not given this information, doing this drawing is impossible. And even if the acceleration is given, one way to get an accurate drawing is to resolve vectors, perhaps rotate the axis to to align with the resultant force and solve some equations of motion in the new axis, clearly not expected of a HSC student.
You could easily work out acceleration from what you have been given if you had a protractor..

Force acting down on mass = mg

Ficticious force acting to right of mass = ma

Tan theta = ma/mg

Tan theta = a/g

a = g*(Tan Theta)

#### nelsonzheng

##### New Member
The ball should go in the other direction.. As the mass is hanging to the right, this means that the train is accelerating to the left, therefore the ball should bounce to the right
Yes, if the train continues to accelerate at a greater or equal rate to the moment depicted in this picture then yes, you're right.
However, this question doesn't specify =(

#### Physics_FTW

##### New Member
Also, im thinking the motion of the ball would look more like this:

http://img18.imageshack.us/i/trainmi.jpg/Initially velocity would be along the same line as the angle made from the horizontal? As train accelerates this angle would increase me thinks

Last edited:

#### k02033

##### Member
Whether or not the motion is towards the left or right again depends on the magnitude of the acceleration. The acceleration could be strong enough to compact the motion such that its bend to the right like your last drawing. But it could also be weak enough so that it only compacts the motion a little making motion to the left possible too. So Both left and right motion could be right since we don't know the acceleration. Your protractor trick is interesting (good thinking) but wont work because you forgot to factor in the tension of the string.

It should be:

Tcos@-ma=0
Tsin@-mg=0

Where T is the tension of the string.

If you neglect the tension then the mass wouldnt even be where it is, it would just fall.

Oh and to complicate the matter even more, the motion will also depend on the velocity of the train at the time the string is cut. And this could be anything, could be nearing the speed of light for all we know. And if this is true then all the answers we have given thus far are all wrong lol. So really the question should have said something like "the train is travelling much slower than light"

#### Fizzy_Cyst

##### Well-Known Member
Hello little brother.

Here are my thoughts:

The angle that the string is subtending to the vertical is less than 45degrees, therefore this means that acceleration due to gravity > acceleration of the train

k02033:

Youve got ur eqns around the wrong way, It should be Tsin@ - ma = 0 and TCos@ - mg = 0

i.e., Tsin@ = ma and TCos@ = mg

ma/mg = a/g = Tsin@/TCos@ = Tan@

Therefore a = gTan@, as my little bro said

Now, the fact that the angle is less than 45degrees (by inspection) tells us that the acceleration of the train < acceleration due to gravity, so it should look similar to a projectile being 'pushed off a cliff' except, initial velocity of the projectile would be in line with the angle subtended at the vertical.

The picture that my little bro drew is what it would look like if acceleration of the train > acceleration due to gravity

Surely you would not have to do all that in the question though. Next they'll ask you to do a conical pendulum...

Btw, there is no possible way the ball could start bouncing to the left unless the train started to accelerate to the right after the string was cut.

Speed of the train really wouldnt matter (until you approach c), as you are worried about relative velocity, rather than absolute velocity.

But again, as was previously said would be different for people observing from different frames of reference :\
i.e., person outside will see ball fall straight down, but will see train move forward. Person inside will see ball fall at the angle subtended at the vertical and curve parabolically.

Meh, crap question if u ask me

Last edited:

#### jyu

##### Member
I did not look at the other information given in the question. I have made many assumptions in the following answers.

a. Why does the mass hang with the string at an angle to the vertical?

Due to the appearance of a horizontal fictitious force on the mass while the train is moving to the right and it is slowing down, or while the train is moving to the left and it is speeding up.
Another possibility: There is a real constant horizontal force acting on the mass, e.g. a fan is blowing horizontally at the mass while the train is stationary or moving at constant velocity.
To an observer inside the train the mass is at rest and the net force (sum of tension force, force of gravity and the horizontal force) is zero.

b. The string then breaks and the mass falls. Indicate the path of the mass on the diagram above. Explain why the mass has taken this path.

When the string breaks, the tension force disappears and there is now a constant net force (sum of force of gravity and the horizontal force) which is equal in magnitude but opposite in direction to the tension force. To the observer inside, because the mass is initially at rest, so it moves in a straight line in the direction of the net force, i.e. in the direction opposite to the tension force before the string breaks.

When you draw the path with the train as the background, you draw what the inside observer sees.

Last edited:

#### jyu

##### Member
Also, im thinking the motion of the ball would look more like this:

http://img18.imageshack.us/i/trainmi.jpg/Initially velocity would be along the same line as the angle made from the horizontal? As train accelerates this angle would increase me thinks

My humble opinion:

Your path is right if the magnitude of the train's acceleration increases (or the fan blowing stronger at the mass) after the breakage of the string.