A golf ball of mass 125g hits a billards ball of mass 172.5g that is initially at rest. after the colision, the golf ball moves to the right at a speed of 10cm/s. the billards ball moves to the left with a speed of 58 cm/s. (a) What was the velocity of the golf ball before the collision? (b) What is the change in total kinetic energy of the system at the collision?
125g = 0.125kg,
172.5g = 0.1725 kg.
a. M1*V1 + M2*V2 = M1*V3 + M2*V4.
0.125*V1 + 0.1726*0 = 0.125*0.10 - 0.1725*0.58.
0.125V1 = 0.0125 - 0.10 = -0.0875,
V1 = -0.70 m/s. = 0.70 m/s To the left.
To answer these questions, we need to apply the principles of conservation of momentum and conservation of kinetic energy.
(a) Velocity of the golf ball before the collision:
The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Mathematically, we can express this as:
(m1 * v1) + (m2 * v2) = (m1 * u1) + (m2 * u2)
where:
m1 = mass of the golf ball
m2 = mass of the billiards ball
v1 = velocity of the golf ball after the collision
v2 = velocity of the billiards ball after the collision
u1 = velocity of the golf ball before the collision (what we want to find)
u2 = velocity of the billiards ball before the collision (which is initially at rest)
Plugging in the given values:
m1 = 125g = 0.125kg
m2 = 172.5g = 0.1725kg
v1 = 10cm/s = 0.1m/s
v2 = -58cm/s (negative because it moves in the opposite direction) = -0.58m/s
u2 = 0m/s (initially at rest)
Using the conservation of momentum equation, we can solve for u1:
(0.125 * 0.1) + (0.1725 * -0.58) = (0.125 * u1) + (0.1725 * 0)
Simplifying the equation:
0.0125 - 0.10005 = 0.125u1
-0.08755 = 0.125u1
u1 ≈ -0.7 m/s
Therefore, the velocity of the golf ball before the collision was approximately -0.7 m/s.
(b) Change in total kinetic energy of the system at the collision:
The principle of conservation of kinetic energy states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Mathematically, we can express this as:
(0.5 * m1 * v1^2) + (0.5 * m2 * v2^2) = (0.5 * m1 * u1^2) + (0.5 * m2 * u2^2)
Plugging in the given values:
m1 = 0.125kg
m2 = 0.1725kg
v1 = 0.1m/s
v2 = -0.58m/s
u1 = -0.7m/s (calculated in part (a))
u2 = 0m/s (initially at rest)
Using the conservation of kinetic energy equation, we can simplify and calculate the change in total kinetic energy:
(0.5 * 0.125 * 0.1^2) + (0.5 * 0.1725 * (-0.58)^2) = (0.5 * 0.125 * (-0.7)^2) + (0.5 * 0.1725 * 0^2)
Evaluating the equation:
0.0003125 + 0.03049875 = 0.00030625
0.03081125 ≈ 0.031 J
Therefore, the change in total kinetic energy of the system at the collision is approximately 0.031 J.