Hi, can you please help me with this? A system consists of three particles, each

Question

Hi, can you please help me with this?

A system consists of three particles, each of unit mass (i.e. m = 1.0 kg), with positions and velocities as follows: (positions are in unit of meter, velocities are in unit of m/s) r_1, = i + j v_2=2i r_2,=j + k v_2-j r_1= k v_1 = i + j + k Find the position and velocity of the center of mass. Find the linear momentum of the system. Find the kinetic energy of the system Find the value of mv^2_CIN,/2, and compare it to the one in part c) Find the angular momentum about the origin A projectile is fired at an angle of 45degree with initial kinetic energy E_0. (See Figure 2 above) At the top of its trajectory, the projectile explodes with additional energy E_0 into two fragments. One fragment of mass m_1 travels straight down. Find the following. What is the magnitude and direction of the second fragment of mass m_2? What is the magnitude and direction of the first fragment of mass m_1? What is the ratio of m_1/m_2 when m_1 is a maximum?

Explanation / Answer

1. a) position of com = m(r1 + r2 + r3)/m = i + j + j + k + k = i + 2j + 2k
velocity of com = m(2i + j + i + j + k)/m = 3i + 2j + k
b) Linear momentum = 3mVcom = 3*1(3i + 2j + k) = 9i + 6j + 3k
c) KE = 0.5*1*(3^2 + 2^2 + 1^2) = 7 J
d) mv^2cm / 2 = 7 J same as c
e) Angular momentum about origin = M(R X v)
1*(1i + 2j + 2k)x(3i + 2j + k) = 2k - j - 6k + 2i + 6j - 4i = -2i + 5j - 4k

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