Final answer:
The speed of the block after the collision is approximately 0.336 m/s. This is calculated using the conservation of momentum principle since the total momentum before and after the collision must be equal in a frictionless environment where the objects stick together.
Step-by-step explanation:
To determine the speed of the block after the collision when a ball of clay hits it, we use the principle of conservation of momentum. This principle states that the total momentum before the collision must be equal to the total momentum after the collision for a system where no external forces are acting, such as friction.
The formula for the conservation of momentum is:
m1 × v1 + m2 × v2 = (m1 + m2) × v_final
Where m1 and v1 are the mass and velocity of the clay ball, and m2 and v2 are the mass and velocity of the block. After the collision, the ball and block stick together, moving with a common velocity v_final.
Given that m1 = 0.051 kg, v1 = 6.6 m/s (for the clay ball), and m2 = 1.0 kg, v2 = 0 m/s (for the block at rest), we can substitute these values:
0.051 kg × 6.6 m/s + 1.0 kg × 0 m/s = (0.051 kg + 1.0 kg) × v_final
Solving for v_final we get:
v_final = (0.051 kg × 6.6 m/s) / (0.051 kg + 1.0 kg)
v_final ≈ 0.336 m/s after the collision.