Conservation of Mechanical Energy in a ball of clay

The correct equation should be:(.5)(m_1)(v_0)^2 \neq (.5)(m_1)(v_1)^2 + (.5)(m_1)(v_1)^2 This shows that the final kinetic energy (KE) is not equal to the initial KE, indicating that mechanical energy is not conserved in this collision. To find the percentage of energy lost, we can use the formula:Percentage loss = [(Ei -Ef)/Ei]*100Where Ei is the initial KE and Ef is the final KE. By plugging in the values for Ei and Ef, we can find the percentage of energy lost.
  • #1
octahedron
37
0

Homework Statement



A 50 g ball of clay traveling at speed [tex]v_0[/tex] hits and sticks to a 1.0 kg block sitting at rest on a frictionless surface.

a. What is the speed of the block after the collision?
b. Show that the mechanical energy is not conserved in this collision. What percentage of the ball's initial energy is "lost?"

The Attempt at a Solution



For part (a), I just said

m_1*v_0 = (m_1 + m_2)*v_1

0.05*v_0 = (0.05+1)*v_1

v_0 = 21*v_1

I'm hoping this is correct! Now, part (b) I'm not entirely sure of. I guess there is no PE in this case so I should show that

(.5)(m_1)(v_0)^2 [tex]\neq[/tex] (.5)(m_1)(v_0)^2 + (.5)(m_1)(v_1)^2

Is this it? How do I go on about finding the percentage "lost"?
 
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  • #2
octahedron said:
For part (a), I just said

m_1*v_0 = (m_1 + m_2)*v_1

0.05*v_0 = (0.05+1)*v_1
This is fine.
v_0 = 21*v_1
Not sure what happened here. Find v_1 in terms of v_0.

I'm hoping this is correct! Now, part (b) I'm not entirely sure of. I guess there is no PE in this case so I should show that

(.5)(m_1)(v_0)^2 [tex]\neq[/tex] (.5)(m_1)(v_0)^2 + (.5)(m_1)(v_1)^2
This expression seems a bit mixed up. Find the initial KE (the left hand side). Find the final KE (you'll need the speed of the combined masses from part a). (Express everything in terms of v_0.)

Compare the two KEs and find their difference (the loss of KE). Then you can figure out what percentage of the original KE that loss is.
 
  • #3
Is the right side of the equation your after? If it is, v_0 shouldn't figure into it, I don't believe.
 
  • #4
Initial KE = Ei = 0.5*m1*Vo^2
Final KE = Ef = 0.5*(m1 + m2 )*V1^2
Show that Ef is not equal to Ei. And percentage loss = [(Ei -Ef)/Ei]*100
 
  • #5
Thanks everyone, got it! :)

Supernats said:
Is the right side of the equation your after? If it is, v_0 shouldn't figure into it, I don't believe.
Oops! I didn't mean to include v_0 there. Sorry for the confusion.
 

1. How is mechanical energy conserved in a ball of clay?

The conservation of mechanical energy in a ball of clay refers to the principle that the total amount of mechanical energy (kinetic energy + potential energy) remains constant as the ball undergoes deformation, as long as no external forces (such as friction or air resistance) act on the system.

2. What factors affect the conservation of mechanical energy in a ball of clay?

The conservation of mechanical energy in a ball of clay is affected by several factors, including the initial velocity of the ball, its mass, the surface it is dropped onto, and the elasticity of the clay. These factors determine the amount of kinetic and potential energy present in the system.

3. Can mechanical energy be lost in a ball of clay?

In theory, mechanical energy cannot be lost in a ball of clay as long as no external forces are acting on the system. However, in real-world scenarios, some mechanical energy may be lost due to factors such as air resistance, friction, or deformation of the clay. This means that the total amount of mechanical energy may decrease, but it is not lost entirely.

4. How does the law of conservation of energy apply to a ball of clay?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another. In a ball of clay, the initial kinetic energy is transformed into potential energy as the ball deforms upon impact. The total amount of energy in the system remains constant, demonstrating the principle of energy conservation.

5. Why is the conservation of mechanical energy important in a ball of clay?

The conservation of mechanical energy is important in a ball of clay because it helps us understand and predict the behavior of objects in motion. It allows us to calculate the final velocity or height of the ball after impact, and is a fundamental principle in the study of mechanics. Additionally, it demonstrates the universal law of energy conservation, which is a crucial concept in physics and the natural world.

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