Phun with Physics

[xcellerate]

Okay so my roommate is taking physics 101 this semester. Yay for him. Now he just called me over to help him with his homework, so arrogantly i thought 'sure i can help you!' ..oops

"Suppose that the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? "

...right, maybe question 2?

"A displacement is related to time as x = Asin(2ft), where A and f are constants. Find the dimensions of A. [Hint: A trigonometric function appearing in an equation must be dimensionless.]"


uhh, alright, i'll be the first to admit i'm an idiot, but what is going on. Displacement i'm figuring is maybe a fancy word for distance? But what are the dimensions? What is going on, because i'm so lost i'm curious.

Normally the physics problems i see are like an open bag of sand sliding down an incline, what the heck is this?

(and i want to look smart by knowing the answer)

 

[Adabiviak]

Is the first expression x=Bt²?
Displacement as a function of time is a measurement of speed/velocity. If the 't' in your expression is a measurement of time, 'B' is your speed/velocity. If the 2 is an exponent, this object would appear to be accelerating.

Given the 'hint' from the teacher, the A in the second equation would have to again be your speed/velocity.

 

[Dan]

B is a dimension of velocity.

A is in units of displacement

displacement is the vector for distance

A can't be velocity because the triginometric function is dimensionless. If you look at the contents of the sin funciton. It's f and t. frequency is 1/s and time is s so the contents are dimensionless.

 

[Dan]

The 2nd year mechanical engineering we have all sorts of crap about damped vibrations. Also, some of the mechanics stuff is pretty tough on the noggin. Here's one of the more fun questions:

A cylindrical tank is constructed by cutting a strip of metal and rolling it up in a spiral at an angle theta. Theta is the angle between the seam of the strip and the longitudinal axis of the cylinder. End caps are stuck on it. The material is held together with some glue and torque is applied to the ends to hold it shut while the glue dries.

Hot steam at a relative pressure of P is pumped into the tank. The steam melts the glue holding the walls together, but luckily the applied torque is enough to keep the tank together. The endcaps are unaffected by the steam. What is the optimal angle theta that the metal strip should be rolled at? At this angle how much torque (in terms of P) is required to contain the steam.

 

[Adabiviak]

Right, but if the trig function is dimensionless, mustn't the coefficient carry the dimension? If the function returns displacement as a function of time, shouldn't the units be velocity?

 

[Dan]

yeah, the coefficient has to carry the units. The units in this case are displacement. The sin function is dimensionless. It ranges from 1 to -1 depending on the time. Thus the displacement ranges from A to -A.

 

[Adabiviak]

Doesn't the teacher imply velocity as the dimension when the question asks for 'displacement related to time'?

 

[Adabiviak]

Doesn't the teacher imply velocity as the dimension when the question asks for 'displacement related to time'?

 

[Dan]

The teacher (more likely the textbook) is asking for displacement. The displacement is a function of time as described by the equation. The equation x = Asin(ft) describes how displacement is related to time. x is displacement, t is time.