Preparing for a phys final, springs and bouyancy

[Mathephysicst]

Hey all, I am a little confused on this, I was trying to study and these two questions came up... I guess i am confused, I don't know the solutions and I want to know which it is and why...

1. A helium balloon is observed to rise up into the air at the front of the classroom, and is only being held to the ground by a rock. the professor pours liquid nitrogen (77K) onto the balloon. The balloon suddenly drops to the ground. The change in which property of the helium gas caused the balloon to no longer be buoyant?

A. Pressure
B. Volume
C. Temperature
D. Mass
E. None of the above

A pendulum undergoing simple harmonic motion can be described by the expression:
X(t) = .2 sin(π t - .3). what is the magnitude of the maximum angular acceleration of this pendulum?

A. .2 1/s^2
B. .2/π 1/s^2
C. .2π 1/s^2
D. .2π^2
E. none of these.

I have been trying to review these two questions for a while and could use some help.

I feel like 1. should be mass pouring nitrogen onto the balloon, but I was told that was wrong.
2. I said none of these, because I don't know what s is, and on top of that its just two derivatives of the X.

 

[DrewD]

s is probably seconds. Angular accelerations is inverse seconds squared.

 

[Mathephysicst]

so then the solution would be -pi*.2*1/s^2?

 

[Ken G]

A helium balloon is observed to rise up into the air at the front of the classroom, and is only being held to the ground by a rock. the professor pours liquid nitrogen (77K) onto the balloon. The balloon suddenly drops to the ground. The change in which property of the helium gas caused the balloon to no longer be buoyant?

A. Pressure
B. Volume
C. Temperature
D. Mass
E. None of the above

I get "B", because the buoyancy of the balloon comes from the weight of the air it displaces (by its volume) being more than the weight of the balloon plus helium. The balloon keeps the same weight, but when it cools, its volume shrinks, and so it displaces less weight of air and loses buoyancy.

A pendulum undergoing simple harmonic motion can be described by the expression:
X(t) = .2 sin(π t - .3). what is the magnitude of the maximum angular acceleration of this pendulum?

A. .2 1/s^2
B. .2/π 1/s^2
C. .2π 1/s^2
D. .2π^2
E. none of these.

I believe this one is D, though I would just call that "acceleration", not "angular acceleration" (because the equation is for x(t), not theta(t), so it refers to a linear displacement, not an angular one). Just take the second time derivative of x(t)-- each time derivative brings out a factor of whatever that symbol is supposed to be (it looks like it is trying to be pi, but then t is in some strange dimensionless unit, overall the whole question doesn't really seem to make a lot of sense).

 

[Mathephysicst]

the spring one should be D if it had the 1/s^2 right?

 

[Ken G]

That one doesn't make sense unless the funny symbol has units of 1/time all on its own, so then there'd be no need to refer to seconds. However, if the "t" in the formula is intended to really be what most people would call t/(1 second), then the symbol could be "pi" and the answer would need a 1/s^2. I think that question is pretty messed up, or at least the notation and the wording are both rather nonstandard.

 

[haruspex]

It is very strange that 's' should appear, unheralded, in four of the choices.
It is not even clear what X is. You seem to be assuming it's the angle to the vertical, but it sounds more like the horizontal displacement.
Fwiw, if X is the angle and L is the pendulum length then
X'' = -gX/L
X = A.sin(Bt + C), where B^2 = g/L
Hence A = .2, π^2 = g/L
Max positive angular accn occurs at max negative X, i.e. -0.2.
At this point X'' = 0.2g/L = 0.2π^2