A 8.9 kg bowling ball traveling at 16.7 m/s strikes a 1.1 kg bowling pin. The impact slows the bowling ball to 11.4 m/s.
Determine the velocity given to the pin.
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Given:
M1 = 8.9kg, V1 = 16.7 m/s.
M2 = 1.1kg, V2 = 0.
V3 = 11.4 m/s = Velocity of M1 after collision.
V4 = ? = Velocity of M2 after collision.
Momentum before = Momentum after:
M1*V1 + M2*V2 = M1*V3 + M2*V4.
8.9*16.7 + 1.1*0 = 8.9*11.4 + 1.1*V4,
V4 = ?
To determine the velocity given to the pin, we can use the principle of conservation of momentum. According to this principle, in the absence of external forces, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. We can use this formula to find the momentum of the bowling ball before and after the collision:
Momentum of the bowling ball before collision = mass of the bowling ball * velocity of the bowling ball
Momentum of the pin = mass of the pin * velocity of the pin
Using the conservation of momentum principle, we can write the equation:
Momentum before collision = Momentum after collision
(mass of the bowling ball * velocity of the bowling ball) + (mass of the pin * velocity of the pin) = (mass of the bowling ball * final velocity of the bowling ball) + (mass of the pin * final velocity of the pin)
Now, let's plug in the values we know:
mass of the bowling ball = 8.9 kg
velocity of the bowling ball before collision = 16.7 m/s
mass of the pin = 1.1 kg
final velocity of the bowling ball = 11.4 m/s
With these values, we can rearrange the equation to solve for the unknown velocity of the pin:
(mass of the pin * velocity of the pin) = (mass of the bowling ball * velocity of the bowling ball) - (mass of the bowling ball * final velocity of the bowling ball) + (mass of the pin * final velocity of the pin)
Substituting the given values:
(1.1 kg * velocity of the pin) = (8.9 kg * 16.7 m/s) - (8.9 kg * 11.4 m/s) + (1.1 kg * 11.4 m/s)
Now, we can solve the equation to find the velocity of the pin.