- #1
PhMichael
- 134
- 0
Homework Statement
A simple pendulum that consists of a mass [tex] m [/tex] and a massless cord of length [tex] L [/tex] is hanged on the ceiling of an elevator, which is intially at rest. The pendulum is performing a simple harmonic motion. The energy of the mass (Kinetic energy + potential energy with respect to the lowest point of the mass' trajectory) is [tex] E_{0} [/tex].
The following experiment if performed:
* at [tex] t=0 [/tex], when the mass is in its lowest point along the trajectory, the elevator's acceleration jumps from [tex] a=0 [/tex] to [tex] a=0.75g [/tex], upwards.
* at [tex] t=\frac{T}{4} [/tex] (T being the cycle time), when the mass is in an extremum (highest point), the elevator's acceleration jumps from [tex] a=0.75g [/tex] to [tex] a=1.5g [/tex], upwards.
What is the total energy of the mass at the ened of the experiment, when the acceleration is [tex] a=1.5g [/tex] ? 2. The attempt at a solution
First of all, the upward acceleration defines a "new gravitational acceleration", which is [tex] g_{eff} = a+g [/tex].
At the lowest point the total energy of the mass in Kinetic since the reference point is defined to be there, therefore the "new gravity" doesn't affect the energy.
At the highest point, however, the total energy is Potential because the velocity is zero over there, theresore the corresponding "new gravity" has some effect there.
Now, how can I relate all of these stuff together?
for the 1st experiment, the total energy is: [tex] E_{1} = \frac{1}{2}mv^{2} [/tex]
for the 2nd experiment, the total energy is: [tex] E_{2} = m(g+a)h [/tex]
But how can I make these stuff useful?!
I don't think that I can use the conservation of energy principle since a fictitious force is regarded as an external force for all energy consideration purposes.