Question

A 0.47 kg block of wood hangs from the ceiling by a string, and a 0.070kg wad of putty is thrown straight upward, striking the bottom of the block with a speed of 5.60 m/s. The wad of putty sticks to the block. (Answer on previous exams) How high does the putty-block system rise above the original position of the block Is the kinetic energy of the system conserved during the collision Is the mechanical energy of the system conserved during the collision Is the mechanical energy conserved after the collision

Answer 1

The height is
`h =0.0269 \ m`

The kinetic energy during collision is not conserved

The Mechanical energy during the collision is not conserved

The mechanical energy after the collision is not conserved

Step-by-step explanation:

From the question we are told that

The mass of the block is
`m_b = 0.47\ kg`

The mass of the wad of putty is
`m_p = 0.070 \ kg`

The speed o the wad of putty is
`v_p = 5.60 \ m/s`

The law of momentum conservation can be mathematically represented as

`p_i = p_f`

Where
`p_i` is the initial momentum which is mathematically represented as

`p_i =m_p * v_p`

While
`p_f` is the initial momentum which is mathematically represented as

`p_f = (m_b + m_p)v_f`

Where
`v_f` s the final velocity

So

`m_p v_p = (m_p + m_b) * v_f`

Making
`v_f` the subject

`v_f = (m_p v_p)/(m_b +m_p)`

substituting values

`v_f = ((0.070)*(5.60))/(0.47 + 0.070)`

`v_f = 0.726 \ m/s`

According to the law of energy conservation

`KE = PE`

Where KE is the kinetic energy of the system which is mathematically represented as

`KE = (1)/(2) (m_p + m_b)v_f^2`

And PE is the potential energy of the system which is mathematically represented as

`PE = (m_p +m_b) gh`

So

`(1)/(2) (m_p + m_b)v_f^2 = (m_p +m_b) gh`

Making h the subject of the formula

`h = (v_f^2)/(2g)`

substituting values

`h = ((0.726 )^2 )/(2 * 9.8)`

`h =0.0269 \ m`

Now the kinetic energy is conserved during collision because the system change it height during which implies some of the kinetic energy was converted to potential energy during collision

The the mechanical energy of the system during the collision is conserved because this energy consists of the kinetic and the potential energy.

Now after the collision the mechanical energy is not conserved because the external force like air resistance has reduced the mechanical energy of that system