Inelastic Collision - Kinetic Energy

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SUMMARY

The discussion focuses on the calculations involved in an inelastic collision between a 6.0kg metal ball and a 6.0kg clay ball. The metal ball, initially moving at 4.0m/s, collides with the stationary clay ball, resulting in both moving together at 2.0m/s. Key calculations include the initial kinetic energy of the metal ball (48J), the final kinetic energy of both balls after the collision (12J each), and the energy lost by the metal ball (36J) while the clay ball gains 12J. The participants clarify the correct approach to calculating kinetic energy loss and gain, emphasizing that while kinetic energy cannot be negative, the change in kinetic energy can be negative, indicating a loss.

PREREQUISITES
  • Understanding of kinetic energy formula: KE = 1/2mv²
  • Knowledge of inelastic collisions and conservation of momentum
  • Ability to perform basic algebraic calculations
  • Familiarity with the concept of energy transfer during collisions
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  • Study the principles of conservation of momentum in inelastic collisions
  • Learn about energy loss in different types of collisions
  • Explore advanced kinetic energy calculations in multi-object systems
  • Investigate real-world applications of inelastic collisions in physics
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Physics students, educators, and anyone interested in understanding the mechanics of collisions and energy transfer in physical systems.

JayaSuria
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A 6.0kg metal ball moving at 4.0m/s hits a 6.0kg clay ball at rest and sticks to it. The two move at 2.0m/s.

a. calculate the kinetic energy of the metal ball before it hits the clay ball.
b. calculate the kinetic energy of the metal ball after it hits the clay ball.
c. calculate the kinetic energy of the clay ball after being hit.
d. calculate the energy that the metal ball lose in the collision.
e. calculate the kinetic energy that the clay ball gain in the collision.

I have answered (a), how to do (b) - (e)?? Plz help
 
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How did you solve (a)?
 
@Doc Al == KE = 1/2mv^2.
(a) KE = 1/2 * 6 * 4^2 , equals to 48J
 
JayaSuria said:
@Doc Al == KE = 1/2mv^2.
(a) KE = 1/2 * 6 * 4^2 , equals to 48J
Good. Now use that same formula to do the rest.
 
Doc Al said:
Good. Now use that same formula to do the rest.

@Doc Al , that's the hiccup. For inelastic collision, after the hit, how to calculate for separate objects as before collision? In that case, is the value in (b) same as (c)?
 
JayaSuria said:
@Doc Al , that's the hiccup. For inelastic collision, after the hit, how to calculate for separate objects as before collision? In that case, is the value in (b) same as (c)?
The mass of each is the same but the velocity changes. You are given the velocity before and after the collision, so just plug away into the formula to compute the KE of each before and after the collision. Then you can figure out how the energy changes.
 
Doc Al said:
The mass of each is the same but the velocity changes. You are given the velocity before and after the collision, so just plug away into the formula to compute the KE of each before and after the collision. Then you can figure out how the energy changes.

@Doc Al owh thanks doc. Is this the solution?
(b) 1/2 * 6 * 2^2
(c) 1/2 * 6 * 2^2
(d) initial 48J, after 12J. Metal ball lost 36J
(e) initial 0J, after 12J. Clay ball gained 12J
 
JayaSuria said:
@Doc Al owh thanks doc. Is this the solution?
(b) 1/2 * 6 * 2^2
(c) 1/2 * 6 * 2^2
(d) initial 48J, after 12J. Metal ball lost 36J
(e) initial 0J, after 12J. Clay ball gained 12J
Looks good to me.
 
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Hi Doc, can u show me the calculation of kinetic energy loss by the metal ball?
Is there any calculation to this? instead by stating it only? for example KEloss=K1 - K2?
where k1 = intial KE of Metall Ball 48 J and K2 after collision 12 J, KEloss= 48-12 = 36 J
but if we do the same for clay ball where we calculate the KE gained by Clay ball using this formula
Kc1 = Kc1 intial KE which is Zero since the clay ball remain stationary, Kc2 = 12 J since it move together with the metal ball at 2.0 m/s
KEgain = Kc1 - Kc2
= 0 - 12 J
= - 12 J , As far as i know, Joule can never be negative, if we change the equation to Kc2-Kc1 we will get the right answer for the clay ball but for the metal ball it would become -36 J (which still negative numbers,except if I can explain that the negative symbol represent the loss of KE by metal ball, is it accepted that way? or KE can never be a negative numbers?)
 
  • #10
Doc Al said:
Looks good to me.
Hi Doc, can u show me the calculation of kinetic energy loss by the metal ball?
Is there any calculation to this? instead by stating it only? for example KEloss=K1 - K2?
where k1 = intial KE of Metall Ball 48 J and K2 after collision 12 J, KEloss= 48-12 = 36 J
but if we do the same for clay ball where we calculate the KE gained by Clay ball using this formula
Kc1 = Kc1 intial KE which is Zero since the clay ball remain stationary, Kc2 = 12 J since it move together with the metal ball at 2.0 m/s
KEgain = Kc1 - Kc2
= 0 - 12 J
= - 12 J , As far as i know, Joule can never be negative, if we change the equation to Kc2-Kc1 we will get the right answer for the clay ball but for the metal ball it would become -36 J (which still negative numbers,except if I can explain that the negative symbol represent the loss of KE by metal ball, is it accepted that way? or KE can never be a negative numbers?)
 
  • #11
I get it now, KEloss can be represent as KEloss=K1-K2 since we want to look for loss of energy therefore minus the intial, whereas KEgain = Ki + kf = 0 + 12
since we wanted to look for gain in kenetic energy therefore we add them together. Sorry pls ignore what i ask in the above
 
  • #12
hanz said:
I get it now, KEloss can be represent as KEloss=K1-K2 since we want to look for loss of energy therefore minus the intial, whereas KEgain = Ki + kf = 0 + 12
since we wanted to look for gain in kenetic energy therefore we add them together. Sorry pls ignore what i ask in the above
Surely, KE can never be negative. But the change in KE, which is always KEf - KEi, can be negative or positive depending on whether energy is lost or gained. (KEf + KEi has no meaning.)
 
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  • #13
Doc Al said:
Surely, KE can never be negative. But the change in KE, which is always KEf - KEi, can be negative or positive depending on whether energy is lost or gained. (KEf + KEi has no meaning.)
means it would be ok if metal ball KEloss=KEf-KEi= 12-48= -36 J? then just explain why it is negative?
 
  • #14
hanz said:
means it would be ok if metal ball KEloss=KEf-KEi= 12-48= -36 J?
The change in KE = - 36 J.

hanz said:
then just explain why it is negative?
A negative change means that the KE decreased. You can say that the metal ball lost 36 J of KE.
 
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