Two balls are approaching each other head on. Their velocities are + 9.55 and -11.0 m/s
(a) Determine the velocity of the center of mass of the two balls if they have the same mass.
(b) Determine the velocity of the center of mass of the two balls if the mass of one ball(v=9.55m/s) is twice the mass of the other ball (v=11.0m/s)
(a) mv1 + mv2 = 2m V
where v is the center-of-mass velocity
V = (v1 + v2)/2 = -1.45/2 = -0.725 m/s
(b)2mv1 + v2 = 3m V
solve for V
The second equation of part be should be 2mv1 + mv2=3mV. 2m(9.55)+(-11m)=3mV which is equal to 19.1m-11m=3mV which is equal to 8.1m=3mV now divide both sides by 3m (where the m's cancel out)and you get V= 2.7 m/s
To determine the velocity of the center of mass of the two balls, we'll use the formula mv1 + mv2 = 2mV, where m is the mass and v is the velocity of each ball, and V is the velocity of the center of mass.
(a) If the balls have the same mass, let's assume the mass of each ball is m. The velocities are +9.55 m/s and -11.0 m/s.
Plugging in the values into the formula:
(9.55m) + (-11.0m) = 2mV
Simplifying the equation:
-1.45m = 2mV
To find V, we divide both sides of the equation by 2m:
V = -1.45/2m
V = -0.725 m/s
Therefore, the velocity of the center of mass of the two balls is -0.725 m/s.
(b) If the mass of one ball (v=9.55 m/s) is twice the mass of the other ball (v=11.0 m/s), let's assume the mass of the first ball is 2m and the mass of the second ball is m.
Plugging in the values into the formula:
(2m)(9.55 m/s) + (m)(-11.0 m/s) = 3mV
Simplifying the equation:
19.1m - 11.0m = 3mV
Combining like terms:
8.1m = 3mV
To find V, we divide both sides of the equation by 3m:
V = 8.1m / 3m
V = 2.7 m/s
Therefore, the velocity of the center of mass of the two balls is 2.7 m/s.