Calculating theta(t): Mass, M & B Variables

In summary, the problem involves calculating theta(t) for a system to remain balanced, with the lower mass initially at zero and theta initially at 90 degrees. Water is poured into the lower mass, causing its mass to increase to Bt. The answer for theta(t) is arccos((Bt)/M), in terms of M and B. The person asking the question also notes their uncertainty about the angle and receives confirmation that their answer is correct.
  • #1
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Homework Statement



See the Question Below For Diagram

In the diagram below, calculate theta(t) such that the system remains balanced. The mass of the lower mass is initially zero and theta is initially 90 degrees, but water is poured into the lower mass such that m(t) = Bt. Answer in terms of M and B.

Homework Equations





The Attempt at a Solution



I was just wondering if my work was right. I got theta(t) = arccos((Bt)/M). I'm sort of unsure if I got the angle correct for the x component of gravity sense normally the angle that we are concerned with is level with the ground and at the bottom of the ramp and not the top.
 

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  • #2
Good observation. Your answer looks good!
 
  • #3
Alright thanks I wasn't sure because I never solved a problem like that before were the angle I was concerned with was not the one that was on the ground.
 

FAQ: Calculating theta(t): Mass, M & B Variables

What is theta(t)?

Theta(t) is a variable used in scientific calculations to represent the angle or angular displacement of an object at a specific time, t. It is typically measured in radians or degrees.

How do you calculate theta(t)?

Theta(t) can be calculated using the formula theta(t) = (M/B) * t, where M is the mass of the object and B is a constant variable that represents the resistance to rotation.

What are the units for theta(t)?

The units for theta(t) will depend on the units used for the mass (M) and B variables. However, theta(t) is typically measured in radians or degrees.

How do the mass and B variables affect theta(t)?

The mass (M) and B variables play a crucial role in determining the value of theta(t). A higher mass will result in a larger value of theta(t), while a higher B variable will result in a smaller value of theta(t).

Can theta(t) be negative?

Yes, theta(t) can be negative. This would indicate that the object is rotating in the opposite direction of the chosen reference point. However, it is common to use absolute values when working with theta(t) to avoid confusion.

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