Calculating Center of Gravity and Mass

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Questions and Answers

What are the coordinates of the center of mass (COM) given in the problem?

(4.31, 4.72) (correct)

(4.5, 4.0)

(3.0, 5.5)

(5.0, 6.1)

What formula is used to calculate the center of mass in a linear system with at least two masses?

Total distance minus the origin distances

Sum of the weighted positions divided by total mass (correct)

Average of the distances from the origin

Sum of the coordinates divided by the number of coordinates

What does the distance from the centroid to the plotted origin influence?

It alters the total mass of the system.

It changes the mass distribution in the system.

It directly affects the centroid's computed location. (correct)

It has no effect on the location of the center of mass.

What is the denominator used to calculate the x-coordinate of the center of mass?

98.43 Signup and view all the answers

Which of the following mathematical operations is NOT used in calculating the coordinates of the center of mass?

Subtraction from total mass Signup and view all the answers

What issue arises when comparing the computed centroid locations?

The values can be inconsistent with their physical representation. Signup and view all the answers

What is the primary reason for discrepancies in the computed centroid and plotted origin?

The centroid's location depends on distance considerations. Signup and view all the answers

What effect does moving the origin further from the centroid have on its computed location?

It raises the computed location. Signup and view all the answers

What is the term used for the center of mass when influenced by gravity?

Center of gravity Signup and view all the answers

Why is determining the center of mass important in physics?

It is critical for determining an object's toppling stability. Signup and view all the answers

Which figure can be divided into units for calculating the center of gravity?

A complex shape composed of multiple figures Signup and view all the answers

When determining the centroid of a rectangle, which formula is utilized?

C = (Σm_ix_i) / M Signup and view all the answers

For a semicircle, what must be considered when calculating its centroid?

It depends on how the circle is bisected. Signup and view all the answers

What additional method should be applied for calculating the centroid of a quarter circle?

Use a modified semicircle formula. Signup and view all the answers

What is the sum of the areas of all unit figures considered when calculating the center of gravity represented as in the formula?

Σ m_i Signup and view all the answers

Which of the following figures is NOT mentioned in the context of calculating the center of mass?

Hexagon Signup and view all the answers

What is the primary definition of collision?

The brief, simultaneous interaction between two or more bodies due to internal forces. Signup and view all the answers

How is specific impulse defined when considering impulse per mass?

The exhaust velocity divided by mass. Signup and view all the answers

In the context of specific impulse, how is it defined when considering impulse per weight?

The exhaust velocity divided by gravity. Signup and view all the answers

What law applies to the concept of momentum within a system?

Conservation of Momentum Signup and view all the answers

Which of the following correctly describes exhaust velocity's role?

It is essential for effective thrust and efficient propellant use. Signup and view all the answers

How does the Conservation Law apply to momentum in a system?

The vector sum of all momenta remains constant, regardless of individual interactions. Signup and view all the answers

If one object has a certain momentum, what must be true about other objects in the system?

They must have the same momentum, but in the opposite direction. Signup and view all the answers

What does the formula $J_s = \frac{J}{m}$ signify in terms of specific impulse?

Impulse per unit mass Signup and view all the answers

What happens to the smaller projectile during an elastic collision?

It rebounds at the same speed in the opposite direction. Signup and view all the answers

In a head-on elastic collision with equal masses, what is the outcome for both projectiles?

The first projectile stops, and the second moves at the same speed as the first. Signup and view all the answers

What defines a non-head-on collision?

The projectile hits the target at a certain angle. Signup and view all the answers

If a projectile of mass $m_1$ collides with a target of mass $m_2$ where $m_1 > m_2$, what is the relationship between their final velocities after the collision?

$v_{1f} ightarrow v_{1}$ and $v_{2f} ightarrow 2v_{1}$. Signup and view all the answers

What characterizes the velocity of the target after a head-on elastic collision?

It moves at a speed equal to that of the first projectile. Signup and view all the answers

What is the typical outcome when two projectiles of equal mass collide elastically head-on?

One projectile stops, while the other continues at original speed. Signup and view all the answers

In what scenario would the final velocity of a smaller mass $m_2$ after a collision be significantly greater than that of a larger mass $m_1$?

When $m_1$ collides with a stationary $m_2$ and transfers its entire momentum. Signup and view all the answers

What happens to the velocity of the first object ($v_{1}$) during an elastic collision where $m_1 < m_2$?

It continues moving in the same direction but at a reduced speed. Signup and view all the answers

What formula should be used for the area of a quarter ellipse if bisected along the x-axis?

$L = 2r\theta$ Signup and view all the answers

If a parabola lies along the y-axis, what is the correct formula for $x_{ii}$?

$x_{ii} = \frac{3y}{5}$ Signup and view all the answers

What is the expression for the centroid of a spandrel given the dimensions provided?

$C_{M_y} = \frac{464.73}{98.43}$ Signup and view all the answers

What area formula applies if the ellipse is bisected along the y-axis?

$x_{ii} = r\theta$ Signup and view all the answers

Which formula correctly represents the area in the context of the parabolic segment given it lies along the x-axis?

$A_{PPP} = \frac{3x}{8}$ Signup and view all the answers

What value must be calculated to find the center of mass using the area of subdivided figures?

Centroid values of all sections Signup and view all the answers

In which scenario is the formula $y_{ii} = \frac{8}{3x}$ applicable?

When a parabola lies along the x-axis Signup and view all the answers

What is the correct expression used in calculating the centroid of the figures?

$C_{M_y} = \frac{72 + 192 + 106.67 + 162.5 + 13.3}{98.43}$ Signup and view all the answers

Which value represents the area of the ellipse if using the formula $A = rac{(A_e)}{2}$?

$A = \pi$ Signup and view all the answers

When applying the formula $C_{M_y} = \frac{4n + 2}{n + 2}$, what condition must hold true?

The shapes must be symmetrical Signup and view all the answers

If the area formula for a spandrel summarizes to $A = [(36)(2)] + [(32)(6)]$ and further terms, what does this represent in practical terms?

Sum of individual section areas Signup and view all the answers

In context to geometry, if one refers to $C_{M_x} = \frac{L}{n + 1} + \frac{2}{n + 1}$ what does it aim to represent?

X-coordinate of the centroid Signup and view all the answers

What is derived from the expression $L_{parabola} = \frac{2b h}{3}$?

Length of the parabolic curve Signup and view all the answers

Study Notes

Center of Gravity

The center of gravity is a point where gravity acts the strongest on an object or system.
Finding the center of mass is important for determining an object's toppling stability.