An industrial die machine is used to stamp out holes in pieces of sheet aluminum. the die strikes the surface of the street of metal at a speed of 10 m/s, passes through the 0.635 cm thick sheet, reverses its direction, and is again moving at 10 m/s as it passes the top surface of the metal moving upward. What is the average acceleration of the die tool as it passes down through the metal and back up again? What is the direction of that acceleration?

Question

An industrial die machine is used to stamp out holes in pieces of sheet aluminum. the die strikes the surface of the street of metal at a speed of 10 m/s, passes through the 0.635 cm thick sheet, reverses its direction, and is again moving at 10 m/s as it passes the top surface of the metal moving upward. What is the average acceleration of the die tool as it passes down through the metal and back up again? What is the direction of that acceleration?

Thanks!

Answer 1

To find the average acceleration of the die tool as it passes down through the metal and back up again, we can use the equation for average acceleration:

average acceleration = (final velocity - initial velocity) / time

First, let's determine the time it takes for the die tool to pass through the metal and reverse its direction. We know the thickness of the sheet aluminum is 0.635 cm, which we can convert to meters:

thickness = 0.635 cm = 0.00635 m

Next, we can calculate the time it takes for the die tool to pass through the sheet:

time = distance / speed

The distance is equal to twice the thickness of the sheet, since it passes through the sheet twice (downward and upward):

distance = 2 * thickness = 2 * 0.00635 m

Now we can calculate the time it takes:

time = distance / speed = (2 * 0.00635 m) / 10 m/s

Simplifying, we get:

time = 0.0127 s

Now, let's determine the final velocity of the die tool as it passes the top surface of the metal moving upward. We know the initial velocity is 10 m/s, and since the die tool reverses its direction, the final velocity will be -10 m/s.

Using the equation for average acceleration, we can now calculate the average acceleration:

average acceleration = (final velocity - initial velocity) / time
= (-10 m/s - 10 m/s) / 0.0127 s

Simplifying, we get:

average acceleration = -1574.80 m/s²

So, the average acceleration of the die tool as it passes down through the metal and back up again is approximately -1574.80 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which means the die tool is decelerating or slowing down.