Applying the work-energy theorem

AI Thread Summary
The work-energy theorem is applied to determine the final velocity of a branch falling from a 95 m tall tree, starting from rest. The initial kinetic energy (K_1) is zero, and the final kinetic energy (K_2) is expressed as (1/2)*m*v^2. The gravitational work done on the branch can be calculated using w=fd, where f is the force of gravity (9.8 m/s^2) and d is the height (95 m). It is suggested to assume a mass to simplify the calculations, as it will cancel out when solving for the final velocity. The focus remains on finding the final velocity without needing the specific mass value.
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Homework Statement


Use the work-energy theorem to solve.
A branch falls from the top of a 95 m tall tree, starting from rest. How fast is it moving when it reaches the ground? Neglect air resistance.

Homework Equations


work-energy theorem:w_total=K_2-K_1
In this problem, K_1 is 0 since it is starting from rest.
K_2=(1/2)*m*v^2 (?)
w=fd (relevant?)

The Attempt at a Solution


If I use the equations I have above, I end up with w=1/2*m*v_f^2.
However, I am not given a mass. I do not know how to finish the calculation without a mass.
If I use w=fd, I have (9.8 m/s^2)(mass)*(95 m).
I am really stuck.
 
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In addition to the equations you listed, you also need the equation for the force of gravity on a mass.

You are only asked for the final velocity. Assume a mass, and carry through with the equations. Hopefully the mass will cancel out when you solve for the velocity.
 
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