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).