Prior Knowledge Questions (Do these BEFORE using the Gizmo.)A buoy is anchored to the ocean floor. A large wave approaches the b
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The kinetic energy of this block-spring when the block has a speed (v) is given by K.E = 1/2 × (M + m/3)v².
<h3>What is kinetic energy?</h3>Kinetic energy can be defined as a form of energy that is possessed by a person due to its motion or change in speed (acceleration).
<h3>How to calculate kinetic energy?</h3>Mathematically, kinetic energy can be calculated by using this formula:
K.E = 1/2 × mv²
Where:
- K.E represents the kinetic energy.
- m represents the mass.
- v represents the speed or velocity.
Since the mass of a segment of this spring is dm = (m/l) dx, the kinetic energy for each of its segment would be given by:
dK = 1/2 × (dm)Vx²
This ultimately implies that, the kinetic energy of this block-spring when the block has a speed (v) is given by:
K.E = 1/2 × Mv² + 1/2 × ¹∫₀((x²v²/l²)m/ldx
K.E = 1/2 × (M + m/3)v².
Read more on kinetic energy here: brainly.com/question/15848455
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Answer:
Explanation:
Mass: M, Length: L.
The formula that gives center of mass is
In the case of a non-uniform mass density, this formula converts to
where the denominator is the total mass and the nominator is the mass times position of each point on the rod.
We have to integrate the mass density over the total rod in order to find the total mass. Likewise, we have to integrate the center of mass of each point (xσ(x)) over the total rod. And if we divide the integrated center of mass to the total mass, we find the center of mass of the rod:
Here x's are cancelled. Otherwise, the denominator would be zero.