Prediction: Find an equation that relates the speed of the falling mass, just before it hits the bottom of its fall, to the height it has fallen. The variables that may be involved are: the change in height of the falling mass (Δh), moment of inertia of the disk (Idisk), the radius of the spool (rspool), the hanging mass (mhanger), and the acceleration of gravity (g). 1) Draw two diagrams of the situation — one for the initial state (just before the hanger is released) and one for the final state (after the mass has fallen by a height Δh). Label the relevant quantities on your diagrams (see the ‘prediction’ section above for what the relevant quantities might be). 2) As we have done in class, set up a conservation-of-energy problem. Write down the initial energy (just before the hanger is released). What kind(s) of energy is/are available initially? Then write down the final energy (after the hanging mass has fallen by a height Δh). What kind(s) of energy is/are present now? 3) What is the relationship between the angular speed of the disk and the translational (linear) speed of the hanger? 4) Use your answers to 2) and 3) to solve the prediction.
Prediction:
Find an equation that relates the speed of the falling mass, just before it hits the bottom of its fall,
to the height it has fallen. The variables that may be involved are: the change in height of the
falling mass (Δh), moment of inertia of the disk (Idisk), the radius of the spool (rspool), the hanging
mass (mhanger), and the acceleration of gravity (g).
1) Draw two diagrams of the situation — one for the initial state (just before the hanger is
released) and one for the final state (after the mass has fallen by a height Δh). Label the
relevant quantities on your diagrams (see the ‘prediction’ section above for what the
relevant quantities might be).
2) As we have done in class, set up a conservation-of-energy problem. Write down the initial
energy (just before the hanger is released). What kind(s) of energy is/are available
initially? Then write down the final energy (after the hanging mass has fallen by a height
Δh). What kind(s) of energy is/are present now?
3) What is the relationship between the angular speed of the disk and the translational (linear)
speed of the hanger?
4) Use your answers to 2) and 3) to solve the prediction.
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