Recall that the essential matrix E describing the stereo geometry of two calibrated cameras is a function only of the relative r
otation and translational offset between the two cameras. Compute the essential matrix for the following camera configurations.
The Point Grey "Bumblebee" stereo camera is a "simple stereo" system having two cameras side-by-side with their optic axes parallel to each other. The baseline distance between the two cameras is 12 cm.
Compute the values of the 3x3 essential matrix E for this stereo system.
The Point Grey "Bumblebee" stereo camera is a "simple stereo" system having two cameras side-by-side with their optic axes parallel to each other. The baseline distance between the two cameras is 12 cm.
Compute the values of the 3x3 essential matrix E for this stereo system.
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The weight of the meterstick is:
and this weight is applied at the center of mass of the meterstick, so at x=0.50 m, therefore at a distance
from the pivot.
The torque generated by the weight of the meterstick around the pivot is:
To keep the system in equilibrium, the mass of 0.50 kg must generate an equal torque with opposite direction of rotation, so it must be located at a distance d2 somewhere between x=0 and x=0.40 m. The magnitude of the torque should be the same, 0.20 Nm, and so we have:
from which we find the value of d2:
So, the mass should be put at x=-0.04 m from the pivot, therefore at the x=36 cm mark.
and this weight is applied at the center of mass of the meterstick, so at x=0.50 m, therefore at a distance
from the pivot.
The torque generated by the weight of the meterstick around the pivot is:
To keep the system in equilibrium, the mass of 0.50 kg must generate an equal torque with opposite direction of rotation, so it must be located at a distance d2 somewhere between x=0 and x=0.40 m. The magnitude of the torque should be the same, 0.20 Nm, and so we have:
from which we find the value of d2:
So, the mass should be put at x=-0.04 m from the pivot, therefore at the x=36 cm mark.
The kinetic energy of a moving object is given by
where m is the object's mass and v its velocity.
In our problem, the initial kinetic energy is:
while the final kinetic energy is:
So, the kinetic energy lost by Lucy and her bike is
where m is the object's mass and v its velocity.
In our problem, the initial kinetic energy is:
while the final kinetic energy is:
So, the kinetic energy lost by Lucy and her bike is