Answer:
Explanation:
Work is defined as the scalar product of force and distance
W=F•d
Given that
F = 8.5i + -8.5j. +×-=-
F=8.5i-8.5j
d = 2.5i + cj
If the work in the practice is zero, then W=0
therefore,
W=F•ds
0=F•ds
0=(8.5i -8.5j)•(2.5i + cj)
Note that
i.i=j.j=k.k=1
i.j=j.i=k.i=i.k=j.k=k.j=0
So applying this
0=(8.5i -8.5j)•(2.5i + cj)
0= (8.5×2.5i.i + 8.5×ci.j -8.5×2.5j.i-8.5×cj.j)
0=21.25-8.5c
Therefore,
8.5c=21.25
c=21.25/8.5
c=2.5
Answer:
a.
b.
c.
d. The angular acceleration when sitting in the middle is larger.
Explanation:
a. The magnitude of the torque is given by
, being r the radius, F the force aplied and
the angle between the vector force and the vector radius. Since
and so
.
b. Since the relation
hols, being I the moment of inertia, the angular acceleration can be calculated by
. Since we have already calculated the torque, all left is calculate the moment of inertia. The moment of inertia of a solid disk rotating about an axis that passes through its center is
, being M the mass of the disk. If we assume that a person has a punctual mass, the moment of inertia of a person would be given by
, being
the mass of the person and
the distance from the person to the center. Given all of this, we have
.
c. Similar equation to b, but changing
, so
.
d. The angular acceleration when sitting in the middle is larger because the moment of inertia of the person is smaller, meaning that the person has less inertia to rotate.