Calculate the vertical motion of a piece of debris from an explosion

In summary, the conversation discussed the calculation of maximum altitude of a small piece of debris launched upward at a velocity of 5.3 km/s after a huge explosion. The first method involved setting the change in potential energy equal to mgh and deriving an expression of h in terms of velocity and gravitational acceleration. The second method involved using the formula U=-GMm/r to calculate the difference in potential energy between the launch point and the peak of the debris. The conversation also mentioned finding the difference between the initial and final potential energies and considering the altitude above the Earth's surface in the calculation.
  • #1
starstruck_
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< Mentor Note -- thread moved to HH from the technical physics forums (because of a forum issue), so no HH Template is shown >

There was a huge explosion, one small piece of debris was launched upward at v=5.3 km/s. Calculate its maximum altitude.

a) Develop an expression for the maximum altitude assuming the change in potential energy = mgh
b) derive an algebraic expression for the maximum altitude using U= -GMm/r.

For a) I set 1/2mv^2 = mgh, therefore
h= v^2/(2g)

I’m not exactly sure how to work with b.
I wasn’t there for this lecture. This is what I’m assuming and I’m most likely understanding this incorrectly. -GMm/r would be equal to the change in potential energy I guess? Which would be 0- 1/2mv^ = -1/2mv^2? I set that equal to -GMm/r? I’m not completely sure.
 
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  • #2
You have a U0 (potental energy at launch point), then a Ufinal (potential energy at the peak. You need to find the difference between those.
 
  • #3
scottdave said:
You have a U0 (potental energy at launch point), then a Ufinal (potential energy at the peak. You need to find the difference between those.

From what I’m understanding :

Etotal 1= E total2

1/2mv^2 - GMm/r (potential energy assuming it is on the surface when it explodes)

= 0- GMm/r+h where h is its altitude above the surface of the Earth ?
 
  • #4
starstruck_ said:
From what I’m understanding :

Etotal 1= E total2

1/2mv^2 - GMm/r (potential energy assuming it is on the surface when it explodes)

= 0- GMm/r+h where h is its altitude above the surface of the Earth ?
If you mean 0- GMm/(r+h), yes.
 
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Likes scottdave

1. How do you calculate the vertical motion of a piece of debris from an explosion?

To calculate the vertical motion of a piece of debris from an explosion, you can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. You will also need to consider factors such as air resistance and the angle of the explosion.

2. What is the initial velocity in the equation for vertical motion of debris from an explosion?

The initial velocity, or u, in the equation v = u + at, is the velocity at the moment of explosion. This can be the velocity of the debris before it was propelled by the explosion, or the velocity of the explosion itself.

3. How does air resistance affect the vertical motion of debris from an explosion?

Air resistance, also known as drag, can affect the vertical motion of debris by slowing it down. This is because as the debris moves through the air, it collides with air molecules, which creates a force in the opposite direction of motion. This force can reduce the velocity and height of the debris.

4. How do you factor in the angle of the explosion when calculating vertical motion of debris?

The angle of the explosion plays a crucial role in the vertical motion of debris. This is because the angle determines the direction and force of the explosion, which can affect the initial velocity and trajectory of the debris. To factor in the angle, you can use trigonometric equations to calculate the horizontal and vertical components of the initial velocity.

5. Can you predict the exact trajectory of debris from an explosion?

While it is possible to calculate the vertical motion of debris from an explosion, it is challenging to predict the exact trajectory. This is because there are many variables, such as air resistance, angle of explosion, and shape/size of debris, that can affect the motion. However, with accurate measurements and calculations, you can make a reasonable estimation of the trajectory.

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