Why does the sun appear to move across the sky over the course of the day? A. because the sun revolves around Earth B. because E
2 answers:
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Answer:
the period of the physical pendulum is 0.498 s
Explanation:
Given the data in the question;
= 0.61 s
we know that, the relationship between T and angular frequency is;
T = 2π/ω ---------- let this be equation 1
Also, the angular frequency of physical pendulum is;
ω = √(mgL / ) ------ let this equation 2
where m is mass of pendulum, L is distance between axis of rotation and the center of gravity of rod and is moment of inertia of rod.
Now, moment of inertia of thin uniform rod D is;
=
mD²
since we were not given the length of the rod but rather the period of the simple pendulum, lets combine this three equations.
we substitute equation 2 into equation 1
we have;
T = 2π/ω OR T = 2π/√(mgL/) OR T = 2π√(
/mgL)
so we can use =
mD² for moment of inertia of the rod
Since center of gravity of the uniform rod lies at the center of rod
so that L = D.
now, substituting these equations, the period becomes;
T = 2π/√(/mgL) OR T =
OR T = 2π√(2D/3g ) ----- equation 3
length of rod D is still unknown, so from equation 1 and 2 ( period of pendulum ),
we have;
ω = 2π/
OR ω
= √(g/D) OR ω
= 2π√( D/g )
so we simple solve for D/g and insert into equation 3
so we have;
T = √(2/3) ×
we substitute in value of
T = √(2/3) × 0.61 s
T = 0.498 s
Therefore, the period of the physical pendulum is 0.498 s
Given data:
* The height of the bullet is 22 m.
* The speed of bullet in the horizontal direction is 524 m/s.
Solution:
By the kinematics equation, the time taken by the bullet to reach the ground is,
where u_y is the vertical velocity component, t is the time taken to reach the ground, g is the acceleration due to gravity, and h is the height of the bullet,
Substituting the known values,
Thus, the time taken by the bullet to reach the ground is 2.12 seconds.
By the kinematics equation for the horizontal motion, the horizontal range of the bullet is,
where u_x is the horizontal component of the velocity, a is the acceleration along the horizontal direction, t is the time taken to reach the ground and R is the horizontal range,
Substituting the known values,
Thus, the horizontal range of the bullet is 1110.9 meters.
Hence, the bullet hit the ground at 1110.9 meters.