# A 0.400 kg block of wood hangs from the ceiling by a string, and a 0.0700 kg wad of putty is...

## Question:

A 0.400 kg block of wood hangs from the ceiling by a string, and a 0.0700 kg wad of putty is thrown straight upward, striking the bottom of the block with a speed of 5.80 m/s. The wad of putty sticks to the block.

(a) Is the mechanical energy of this system conserved? yes or no

(b) How high does the putty-block system rise above the original position of the block? cm

## The energy in Inelastic collision:

The collision where the objects get stick to each other after the collision, or we can say move as one unit is known as Inelastic collision. In these types of collisions, momentum remains conserved, but energy loss takes place.

Given data

• Mass of the block {eq}(M) = 0.4 \ kg {/eq}
• Mass of the putty {eq}(m) = 0.07 \ kg {/eq}
• Speed of the putty {eq}(u) = 5.8 \ m/s {/eq}

(a)

No,

the energy will not remain conserved.

(b)

Now, applying the conservation of momentum

{eq}mu = (m+M)v \\ 0.07 \times 5.8 = (0.07 + 0.4) v \\ v = 0.864 \ m/s {/eq}

where

• v is the velocity of the block and putty after the collision

Now, applying the energy of conservation after the collision

{eq}\dfrac{1}{2}(m+M)v^{2} = (m+M)gh \\ 0.5 \times (0.864)^{2} = 9.8 \times h \\ h = 0.038\ m {/eq}

where

• h is the height raised