Kinetic/Thermal Energy Problem

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In summary, a 2.0 kg piece of porous volcanic rock is thrown vertically upward with an initial speed of 45 m/s in a volcanic eruption. After traveling upward a distance of 45 m, it begins to fall back to the Earth. The initial kinetic energy of the rock is 1012.5 J. The increase in thermal energy due to air friction during ascent is 1142.1 J. If the increase in thermal energy on the way down is 70% of that on the way up, the speed of the rock when it returns to its initial position is approximately 32.3 m/s. The relevant equations for this problem include K = 1/2 M * V^2, External Work =
  • #1
maniacp08
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In a volcanic eruption, a 2.0 kg piece of porous volcanic rock is thrown vertically upward with an initial speed of 45 m/s. It travels upward a distance of 45 m before it begins to fall back to the Earth.
(a) What is the initial kinetic energy of the rock?

(b) What is the increase in thermal energy due to air friction during ascent?

(c) If the increase in thermal energy due to air friction on the way down is 70% of that on the way up, what is the speed of the rock when it returns to its initial position?

Relevant Equations:
K = 1/2 M * V^2
External Work = Change in Mechanical Energy + Change in Thermal Energy
Change in Thermal Energy = Friction Force * Displacement


Is the answer for part A just
1/2 M * V^2?
It seems a little bit too easy.

For Part B-
Is to find the change in thermal energy during its ascent
Change in Thermal Energy = Friction Force * Displacement
Friction Force = Uk * Normal Force
How would I find Uk or Normal Force?

Any help would be grateful.
 
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  • #2
maniacp08 said:
Is the answer for part A just
1/2 M * V^2?
It seems a little bit too easy.
They can't all be hard.

For Part B-
Is to find the change in thermal energy during its ascent
Change in Thermal Energy = Friction Force * Displacement
Friction Force = Uk * Normal Force
How would I find Uk or Normal Force?
Kinetic friction is a model that applies to dry solids rubbing against each other; it doesn't apply here. Luckily, you don't need it. Consider the total mechanical energy the rock had to start with (part A) and compare it to what's left when it reaches its highest point.
 
  • #3
If I let y=0 when the rock is launched

Ki + Ui = Kf + Uf?

The initial Kinetic energy is 1/2 * M * Vi^2
The initial Potential Energy is 0

Is the Final Kinetic Energy where it reaches its highest point 0 since the final velocity will be 0 at its highest point
The final potential energy is MGH where H is 45m

So I have
1/2 M * Vi^2 = MGH

What am I suppose to solve/find out?
 
  • #4
maniacp08 said:
So I have
1/2 M * Vi^2 = MGH

What am I suppose to solve/find out?

Nothing, you have everything. Did you check if it's true? I mean, are the two sides equal?
I don't think so. Why?
 
  • #5
Ahh, I got it, the difference is 1142.1 J.
Thanks!

For Part C:
(c) If the increase in thermal energy due to air friction on the way down is 70% of that on the way up, what is the speed of the rock when it returns to its initial position?

70% of 1142.1J = 799.47J

Would it be
Ki + Ui = Kf + Uf From the highest point to the initial position?
0 + MGH = 1/2 M * Vf^2 + 0
MGH = 1/2 M * Vf^2

MGH + 799.47 = 1/2 M * Vf^2

and solve for Vf?
 
  • #6
Almost, but you're getting a bit mixed up. Think of the energy this way:

What you start with (PE at the top) = KE at the bottom (1/2MVf^2) + Thermal energy (which you've just calculated)

Rearrange that and solve for Vf.
 
  • #7
Thanks Doc!
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.

2. How is kinetic energy calculated?

The formula for calculating kinetic energy is K.E. = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

3. What is thermal energy?

Thermal energy is the energy that comes from heat. It is the sum of the kinetic and potential energy of the particles that make up a substance.

4. How is thermal energy related to kinetic energy?

Thermal energy and kinetic energy are closely related because thermal energy is the sum of the kinetic energy of the particles in a substance. As the kinetic energy of the particles increases, so does the thermal energy of the substance.

5. How does temperature affect kinetic and thermal energy?

As temperature increases, the kinetic energy of particles also increases. This results in an increase in thermal energy. Similarly, as temperature decreases, the kinetic energy of particles decreases, resulting in a decrease in thermal energy.

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