Total Energy Change in a Stamping Machine
What is the change in total energy of a 25-kg hammerhead moving vertically down in a stamping machine?
Change in Total Energy Calculation
The change in total energy of the hammerhead moving vertically down in a stamping machine can be calculated using the given formula:
Change in total energy = \[E_2 - E_1 = m(u_2 - u_1) + \frac{1}{2}m(v^2 - u^2) + mg(h - h')\]
Given data:
Mass of hammerhead (m) = 25 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 50 m/s
Height difference (h - h') = 1 m
Acceleration due to gravity (g) = 9.8 m/s^2
Detailed Explanation
First, we calculate the change in internal energy of the hammerhead:
Change in internal energy = \(m(u_2 - u_1) = 25 \times (50 - 0) = 0\) J (joules)
Next, we substitute the given values into the formula for the change in total energy:
Change in total energy = \(\frac{1}{2} \times 25 \times 50^2 + 25 \times 9.8 \times (-1)\) J
Now, we can calculate the change in total energy:
Change in total energy = 31005 J
Converting Joules to Kilojoules (KJ):
1 KJ = 1000 J
Therefore, the change in total energy of the hammerhead moving vertically down in the stamping machine is 31.005 Kilojoules (KJ).