Spring with 2 masses rotating and vibrating

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SUMMARY

The discussion revolves around a physics problem involving two masses connected by a spring with a stiffness of 400 N/m, where the spring is stretched 0.3 m. The masses are m1 = 1.4 kg with a velocity of <5.5, -5.5, 0> and m2 = 3.4 kg with a velocity of <-13.5, 8, 0>. Participants are tasked with calculating the x and y components of the center of mass velocity (V(center mass)) and the total kinetic energy (K total). Key equations provided include Ktot = K trans + K rel and Psys = M(total)V(cm).

PREREQUISITES
  • Understanding of classical mechanics principles, specifically center of mass calculations.
  • Familiarity with kinetic energy equations, including translational and rotational forms.
  • Knowledge of spring mechanics, particularly Hooke's Law.
  • Ability to perform vector operations in three-dimensional space.
NEXT STEPS
  • Calculate the center of mass velocity using the formula V(cm) = (m1*v1 + m2*v2) / (m1 + m2).
  • Determine the total kinetic energy (K total) using Ktot = K trans + K rel.
  • Explore the implications of spring stiffness on oscillatory motion.
  • Investigate the effects of mass distribution on the dynamics of connected systems.
USEFUL FOR

Students studying classical mechanics, physics educators, and anyone involved in solving problems related to dynamics and oscillations in mechanical systems.

ross0523
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Homework Statement



Consider an object consisting of two balls connected by a spring, whose stiffness is 400N/m.
The object has been thrown through the air
and is rotating and vibrating as it moves. At
a particular instant the spring is stretched
0.3m, and the two balls at the ends of the
spring have the following masses and velocities:

m1= 1.4kg v1= <5.5, -5.5, 0>
m2=3.4 kg v2=<-13.5, 8, 0>

What is x and y components of V(center mass)?
What is K total=?


Homework Equations


Ktot= K trans + K rel
Psys= M(total)V(cm)
U=1/2 kx^2
Ke=1/2 mv^2
Ke= 1/2 I w^2


3. The Attempt at a Solution :

I tried to just solve for center of mass and apply x and y velcoities but it didnt work.
 
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ross0523 said:

Homework Statement



Consider an object consisting of two balls connected by a spring, whose stiffness is 400N/m.
The object has been thrown through the air
and is rotating and vibrating as it moves. At
a particular instant the spring is stretched
0.3m, and the two balls at the ends of the
spring have the following masses and velocities:

m1= 1.4kg v1= <5.5, -5.5, 0>
m2=3.4 kg v2=<-13.5, 8, 0>

What is x and y components of V(center mass)?
What is K total=?


Homework Equations


Ktot= K trans + K rel
Psys= M(total)V(cm)
U=1/2 kx^2
Ke=1/2 mv^2
Ke= 1/2 I w^2


3. The Attempt at a Solution :

I tried to just solve for center of mass and apply x and y velcoities but it didnt work.

What is that supposed to mean? Show your work.
 

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