Final answer:
The speed of the lumps of clay after they stick together is 0.6 m/s.
Step-by-step explanation:
To find the final velocity, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
Momentum is calculated by multiplying mass and velocity. In this case, the total initial momentum is the sum of the individual momentums of the two lumps of clay.
Mass of the first lump of clay (A) = 0.375 kg, velocity of the first lump of clay (A) = 7 m/s
Mass of the second lump of clay (B) = 0.250 kg, velocity of the second lump of clay (B) = -12 m/s (since it is moving to the left)
Momentum before collision = (Mass A * Velocity A) + (Mass B * Velocity B)
Momentum before collision = (0.375 kg * 7 m/s) + (0.250 kg * -12 m/s)
Momentum before collision = 2.625 kg.m/s - 3.000 kg.m/s
Momentum before collision = -0.375 kg.m/s
Since the clay lumps stick together after the collision, we can consider them as one mass moving together.
Let's denote the final velocity of the combined lumps as V.
Momentum after collision = (Mass A + Mass B) * V (since they are moving together)
Momentum after collision = (0.375 kg + 0.250 kg) * V
Momentum after collision = 0.625 kg * V
Since momentum is conserved, we can set the momentum before the collision equal to the momentum after the collision:
-0.375 kg.m/s = 0.625 kg * V
V = -0.375 kg.m/s / 0.625 kg
V = -0.6 m/s
Since the velocity is negative, indicating that the lumps are moving to the left, we can take the absolute value to find the speed:
Speed of the lumps of clay after they stick together = 0.6 m/s