Physics, 26.10.2020 17:00 ashhuizing

The masses mi are located at the points Pi. Find the moments Mx and My and the center of mass of the system. m1 = 5, m2 = 4, m3 = 3, m4 = 6; P1(−4, 3), P2(0, 5), P3(3, 2), P4(1, −2)

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Answer from: sydthekid9044

The center of mass of the system at the given points (-0.278, 1.61).

The given parameters;

masses, $m_1 = 5, \ m_2 = 4, m_3 = 3, m_4 = 6$ positions, $p_1(-4, \ 3), \ p_2(0, \ 5), \ p_3(3, \ 2) , \ p_4(1, \ -2)$

The total mass is calculated as follows;

m = 5 + 4 + 3 + 6 = 18

The sum of the masses on the on x and y-direction;

$M_x = \Sigma M_i y_i\\\\M_x = 5(3) + 4(5) + 3(2) + 6(-2) = 29\\\\M_y = \Sigma M_ix_i \\\\M_y = 5(-4)+ 4(0) + 3(3) + 6(1) = -5$

The center mass is calculated as follows;

$M_y = \frac{29}{18} = 1.61 \\\\M_x = \frac{-5}{18} = -0.278 \\\\(M_x, M_y) = (-0.278, \ 1.61)$

Thus, the center of mass of the system at the given points (-0.278, 1.61).

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Answer from: zianebonankenotdbev

Answer with Explanation:

We are given that

m_1=5,m_2=4,m_3=3,m_4=6

P_1=(-4,3),P_2=(0,5),P_3=(3,2),P_4=(1,-2)

We have to find Mx ,My and center of mass of the system.

$M_x=\sum_{i=1}^{i=n}m_iy_i$

M_x=5(3)+4(5)+3(2)+6(-2)

M_x=29

$M_y=\sum_{i=1}^{i=n}m_ix_i$

M_y=5(-4)+4(0)+3(3)+6(1)

M_y=-5

Total mass,m=m1+m2+m3+m4=5+4+3+6=18

$\bar x=\frac{M_y}{m}=\frac{-5}{18}$

$\bar{y}=\frac{M_x}{m}=\frac{29}{18}$

Center of mass=(-5/18,29/18)

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

Igot 56.55 as the anwer

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The masses mi are located at the points Pi. Find the moments Mx and My and the center of mass of the...