Two balls are approaching each other head-on. Their velocities are +9.30 and -12.1 m/s. Determine the velocity of the center of mass of the two balls for the following conditions. (Use the sign of your answer to indicate the direction.)
(a) They have same mass.
m/s
(b) The mass of one ball (v = +9.30 m/s) is two times the mass of the other ball (v = -12.1 m/s).
m/s
MV+mv=(M+m)v'
so the center of mass v' velocity is moving ALWAYS at (MV+mv)/(totalmass)
Someone answer this question plzzzzz...
To determine the velocity of the center of mass of two approaching balls, we can use the principle of conservation of momentum. The center of mass velocity can be calculated by taking into account the masses and velocities of the two balls.
(a) When the two balls have the same mass:
First, we need to calculate the total momentum of the system. The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
For the first ball with a velocity of +9.30 m/s, and the second ball with a velocity of -12.1 m/s, their momenta are:
p1 = m * 9.30
p2 = m * (-12.1)
Since the two balls have the same mass, the total momentum of the system is:
p_total = p1 + p2 = m * 9.30 + m * (-12.1)
To find the velocity of the center of mass, we divide the total momentum by the total mass of the system. Since the masses are the same, we can combine them:
m_total = m + m = 2m
Now, we can calculate the velocity of the center of mass (v_cm):
v_cm = p_total / m_total = (m * 9.30 + m * (-12.1)) / (2m)
The mass 'm' cancels out, and we are left with:
v_cm = (9.30 - 12.1) / 2
Evaluating the expression:
v_cm = -1.4 m/s
Therefore, the velocity of the center of mass for the two balls with the same mass is -1.4 m/s.
(b) When the mass of one ball is twice the mass of the other:
Following the same steps as before, we calculate the total momentum of the system. However, this time the masses are not the same.
Let's assume the mass of the first ball (v = +9.30 m/s) is 'm1' and the mass of the second ball (v = -12.1 m/s) is 'm2'. Since the mass of one ball is twice the mass of the other, we have:
m1 = 2m2
The momenta for the respective balls are:
p1 = m1 * 9.30
p2 = m2 * (-12.1)
The total momentum becomes:
p_total = p1 + p2 = (2m2 * 9.30) + m2 * (-12.1)
To find the velocity of the center of mass, we divide the total momentum by the total mass of the system:
m_total = m1 + m2
Substituting m1 with 2m2, we have:
m_total = 2m2 + m2 = 3m2
Now, we can calculate the velocity of the center of mass (v_cm):
v_cm = p_total / m_total = [(2m2 * 9.30) + m2 * (-12.1)] / (3m2)
The mass 'm2' cancels out, and we are left with:
v_cm = (2 * 9.30 - 12.1) / 3
Evaluating the expression:
v_cm = 4.50 / 3
v_cm = 1.50 m/s
Therefore, the velocity of the center of mass for the two balls with one ball being twice the mass of the other is 1.50 m/s.