Question: A wad of sticky clay of mass m is hurled horizontally at a wooden block of mass M initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides a distance d before coming to rest. If the coefficient of friction between the block and the surface is , what was the speed of the clay immediately before impact?
The speed of the clay immediately before impact is, .
The linear momentum of an object can be written as
Here, represents the momentum, represents the mass of the particle, represents the speed of the particle.
Mass of the clay, m.
Mass of the block, M.
The coefficient of friction between the block and the surface is .
The distance traveled by block before coming to rest, d.
In this case, the collision is inelastic, which means the total momentum is conserved.
Thus, the total momentum before the impact is equal to the total momentum after the momentum is the same; we can mathematically write this as
From equation (1), we can write the above expression as
Here i and f subscript represent the initial and final values.
Before the impact:
The block is at rest, .
And the clay is moving with a velocity ,
After the impact:
They stick together, behave as a single object, and move with a velocity of .
Substituting the values in equation 2, we get
The kinetic energy of the clay block system after the impact when they are stuck together can be written as
The work done on the system due to the frictional force can be calculated as
Here is the frictional force that is .
This work done and the overall kinetic energy will be equal due to the energy conservation principle, which means
Now, substituting the values in equation 4, we get
From equations 3 and 5, we can write
Thus, the speed of the clay immediately before impact is .
Two particles of different mass start from rest, the same net force acts on both of them as they move over equal distances. How do their final kinetic energies compare?
(a) The particle of larger mass has more kinetic energy.
(b) The particle of smaller mass has more kinetic energy.
(c) The particles have equal kinetic energies.
(d) Either particle might have more kinetic energy.
94% of StudySmarter users get better grades.Sign up for free