Final answer:
To find the mass of the block in this problem, we can use the conservation of momentum. After finding the final velocity of the combined system, we can use this value to determine the mass of the block.
Step-by-step explanation:
In this problem, we have a 5g ball of putty moving horizontally at 10m/s. It collides with and sticks to a block lying on a frictionless horizontal surface. We are given that 16% of the kinetic energy is lost.
To find the mass of the block, we can use the conservation of momentum. Since the ball sticks to the block, the final velocity of the combined system will be zero.
Using the equation:
m1v1 + m2v2 = (m1 + m2)vf
where m1 is the mass of the putty ball, v1 is the initial velocity of the putty ball, m2 is the mass of the block, v2 is the initial velocity of the block, and vf is the final velocity of the combined system.
Plugging in the values, we get:
(0.005kg)(10m/s) + (m2)(0m/s) = (0.005kg + m2)(0m/s)
0.05kg = 0.005kg + m2
m2 = 0.045kg
Therefore, the mass of the block is 0.045kg.