Question

A piston motion moves a 25-kg hammerhead ver tically down 1 m from rest to a velocity of 50 m/s in a stamping machine. What is the change in total energy of the hammerhead?

Answer 1

`\Delta E_(ham) = 31004.825\,J`

Step-by-step explanation:

Let consider that bottom has a height of zero. The change in total energy of the hammerhead is modelled after the Principle of Energy Conservation and Work-Energy Theorem:

`U_(g,A) + \Delta E_(ham) = K_(B)`

`\Delta E_(ham) = K_(B)-U_(g,A)`

`\Delta E_(ham) = (1)/(2)\cdot m_(ham) \cdot v_(B)^(2)-m_(ham)\cdot g \cdot h_(A)`

`\Delta E_(ham) = m_(ham)\cdot ((1)/(2)\cdot v_(B)^(2)-g\cdot h_(A) )`

`\Delta E_(ham) = (25\,kg)\cdot [(1)/(2)\cdot (50\,(m)/(s) )^(2) - (9.807\,(m)/(s^(2)) )\cdot (1\,m)]`

`\Delta E_(ham) = 31004.825\,J`