A mass of 29kg is moving to the right at 15m/s. That mass collides with a 25 kg mass that is stationary. The masses stick together after the collision. What is the velocity of the masses after the collision?
Answer
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A mass of 29kg is moving to the right at 15m/s. That mass collides with a 25 kg mass that is stationary. The masses stick together after the collision. What is the velocity of the masses after the collision
Try applying the law of conservation of momentum. Both masses will be moving to the right after the collision.
To find the velocity of the masses after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. So, let's calculate the initial momentum and final momentum separately.
Initial momentum:
Mass 1 (m1) = 29 kg
Velocity 1 (v1) = 15 m/s
Momentum 1 = m1 * v1
Final momentum:
Mass 2 (m2) = 25 kg
Now, since the masses stick together after the collision,
We can add the two masses to find the combined mass (m).
m = m1 + m2
To find the final velocity (v) of the masses after the collision, we can use the equation:
Momentum 1 + Momentum 2 = Momentum
(m1 * v1) + (m2 * 0) = (m * v)
0 + 0 = (m * v)
Since the second mass is stationary (velocity is zero), the momentum of the second mass is zero.
Thus, the equation simplifies to:
(m1 * v1) = (m * v)
Substituting the given values:
(29 kg * 15 m/s) = (m * v)
435 kg.m/s = (m * v)
Now, substituting the value of m from earlier:
435 kg.m/s = ((29 kg + 25 kg) * v)
435 kg.m/s = (54 kg * v)
Dividing both sides of the equation by 54 kg:
435 kg.m/s / 54 kg = v
v = 8.056 m/s (approximately)
Therefore, the velocity of the masses after the collision is approximately 8.056 m/s to the right.