Calculate the acceleration of each mass at the instant the thread snaps

In summary, the conversation discusses revising the laws of motion and momentum in the context of a suspended lead and copper sphere. The spring constant is not given, but the situation can be treated as an explosion without adding kinetic energy to the masses. The acceleration of the copper sphere can be calculated using the equilibrium position and omega after the string is burned. The lead's acceleration can be calculated by considering the force holding the combined lead and brass before the string is cut. The acceleration cannot be 10m/s as that is not a valid unit for acceleration.
  • #1
Josielle Abdilla
50
4

Homework Statement


A piece of lead of mass 1.5 kg is suspended from a light spring. A copper sphere of mass 2.5 kg is suspended by keans of a thread as attatched to the lead. The thread is then burnt. Calculate the acceleration of each mass at the instant the thread snaps

Homework Equations


(Mv-mu/ t ) of the lead = mv-mu /t of the sphere
 
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  • #2
What is that you are revising? Please show what you have done so far. Is the spring constant given?
 
  • #3
I am revising the laws of motion and momentum. The spring constant is not given So far, I have only guessed that this situation is an explosion but nevertheless I can't think of how is it possible for the copper sphere to adopt an acceleration other than 10m/s. Do you have any ideas about this pls?
 
Last edited:
  • #4
Josielle Abdilla said:
No, I am revising the laws of motion and momentum. The spring constant is not given So far, I have only guessed that this situation is an explosion but nevertheless I can't think of how is it possible for the copper sphere to adopt an acceleration other than 10m/s

Just use ##k## for the spring constant and See what you get.
 
  • #5
I assume that the initial condition is stable and nothing is moving. Then you can figure out how much force the spring is exerting at that position. That gives you its force at the instant that the string is cut. You should be able to calculate the answers from that.
 
  • #6
Josielle Abdilla said:
I am revising the laws of motion and momentum. The spring constant is not given So far, I have only guessed that this situation is an explosion but nevertheless I can't think of how is it possible for the copper sphere to adopt an acceleration other than 10m/s. Do you have any ideas about this pls?
You may treat it as an explosion that doesn't add kinetic energy to the two masses, so the treatment doesn't buy you much. Remeber that in a spring-mass system the acceleration is proportional to the displacement from the equilibrium position, the constant of proportionality being ##\omega^2##. What are the equilibrium position and ##\omega## after the string is burned and the copper sphere drops?
 
  • #7
Maybe I am missing something. I don't see any connection to an explosion. The dropping copper sphere is just being released to fall. The lead is just being pulled by a spring. IMHO, both are simple acceleration problems.
 
  • #8
Josielle Abdilla said:
I can't think of how is it possible for the copper sphere to adopt an acceleration other than 10m/s. Do you have any ideas about this pls?
Do you have a reason for thinking this answer is wrong?
 
  • #9
Josielle Abdilla said:
an acceleration other than 10m/s
It cannot be that since m/s does not express an acceleration.
 
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  • #10
The acceleration of the lead is slightly harder. The spring coefficient is not needed. How much force was holding the combined lead and brass before the string was cut? That force is still there after the string is cut.
 

Related to Calculate the acceleration of each mass at the instant the thread snaps

1. What is the formula for calculating acceleration?

The formula for acceleration is a = (v - u) / t, where "a" represents acceleration, "v" represents final velocity, "u" represents initial velocity, and "t" represents time.

2. How is acceleration related to mass?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a larger mass will require a larger force to achieve the same acceleration as a smaller mass.

3. What does it mean when the thread snaps?

When the thread snaps, it means that the force holding the masses together is no longer present. This results in the masses moving independently, and their acceleration will be determined by the net force acting on each mass.

4. How do I calculate the net force acting on each mass?

To calculate the net force, you need to know the mass of each object and the force acting on it. You can then use Newton's Second Law (F = ma) to calculate the net force acting on each mass, which will determine their acceleration.

5. Can the acceleration of each mass be different at the instant the thread snaps?

Yes, the acceleration of each mass can be different at the instant the thread snaps. This is because the net force acting on each mass may be different, leading to different accelerations according to Newton's Second Law.

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