The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks
along its length. Any one or a combination of the four forces shown can be exerted on the stick as indicated. All four forces are exerted on the stick that is initially at rest. What is the angular momentum of the stick after 2.0s ?
1 answer:
Answer:
After a duration of 2.0 seconds, the angular momentum of the system is .
Explanation:
Let’s denote the forces acting on the rod as A, B, C, and D, and the distance between them as .
The torque produced by force A can be expressed as
,
for force B the torque is
,
the torque for force C is
,
and the torque due to force D is
.
This leads to a total torque on the stick as
Subsequently, this torque results in an angular acceleration in accordance with the formula
where represents the moment of inertia of the stick, which has a value of
.
Thus, the angular acceleration calculates to
.
Now, the angular momentum of the rod is given by
,
where is considered the angular velocity.
Given , we conclude that
Thus, , the angular momentum is
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Answer:
35.79 meters
Explanation:
We have an archer, and there is a target. Denote the distance between them as d.
The bowman releases the arrow, which travels the distance d at a velocity of 40 m/s until it hits the target. We establish the equation as:
Right after this, the arrow produces a muffled noise, traveling the same distance d at a speed of 340 m/s in time . Thus, we can derive:
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Consequently, the sound reaches the archer, precisely 1 second post-firing the bow, resulting in:
.
Using this relationship in the distance formula for sound allows us to write:
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Substituting the value of d from the first equation yields:
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Now, after some calculations, we can proceed further:
.
Finally, the value is inserted into the initial equation: