How Do You Solve This Energy Conservation Problem?

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SUMMARY

The discussion centers on solving an energy conservation problem involving a cylinder and a mass attached to a rope. Key equations include kinetic energy (KE = 0.5mv²) and potential energy (PE = mgh). Participants emphasize the importance of defining the system and analyzing energy at two critical points: before the mass is released and just before it strikes the ground. The total energy of the system must be conserved, incorporating both the linear and rotational kinetic energy of the cylinder.

PREREQUISITES
  • Understanding of kinetic energy and potential energy equations (KE = 0.5mv², PE = mgh)
  • Familiarity with the concept of conservation of energy
  • Basic knowledge of rotational motion and angular velocity
  • Ability to analyze mechanical systems involving pulleys and masses
NEXT STEPS
  • Study the relationship between translational velocity and angular velocity in rotating systems
  • Learn about the principles of rotational kinetic energy and its calculations
  • Explore examples of energy conservation problems in physics
  • Review frictionless pulley systems and their energy dynamics
USEFUL FOR

Students studying physics, particularly those tackling problems related to energy conservation, mechanics, and rotational dynamics.

webdivx
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Homework Statement


http://img172.imageshack.us/img172/5227/4rj8.jpg


Homework Equations


Not sure, but I think KE=.5mv2 and PE=mgh are two possibly useful equations for this problem.



The Attempt at a Solution


I have no idea how to even start this problem. I've been searching the internet for hours and I seriously need help. Step by step instructions on how to do this are really really appriciated.
 
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When using conservation of energy, you have to define the system which is of interest to you. You have a cylinder and a mass attached to the rope. Now, what exactly does conservation fo energy tell you, if you analyse the energies of the system at the point before the release and at the point just before the mass strikes the ground? What kind of energy do the objects in motion possess?
 
radou said:
When using conservation of energy, you have to define the system which is of interest to you. You have a cylinder and a mass attached to the rope. Now, what exactly does conservation fo energy tell you, if you analyse the energies of the system at the point before the release and at the point just before the mass strikes the ground? What kind of energy do the objects in motion possess?

they possesses Kinetic Energy if they are in motion.
 
webdivx said:
they possesses Kinetic Energy if they are in motion.

Exactly. Note that the cylinder possesses rotational kinetic energy, since it has an angular velocity \omega. Find the relation between the translatoral velocity v of the other mass and between the angular velocity of the cylinder, and simply use energy conservation.
 
radou said:
Exactly. Note that the cylinder possesses rotational kinetic energy, since it has an angular velocity \omega. Find the relation between the translatoral velocity v of the other mass and between the angular velocity of the cylinder, and simply use energy conservation.

i don't know how to do that :cry:

please walk me through
 
webdivx said:
i don't know how to do that :cry:

please walk me through

Okay, do you know how to use conservation of energy? The total energy of the system is constant in time, so you can pick two points in time at which you will analyse the system. Let's pick the first point as the point just before the mass on the rope is left to move freely, and the second point as the point just before the same mass falls onto the ground. Now, define the energy of the system (i.e. the sum of potential and kinetic energy) for point 1 and for point 2, and then set them equal.
 
radou said:
Okay, do you know how to use conservation of energy? The total energy of the system is constant in time, so you can pick two points in time at which you will analyse the system. Let's pick the first point as the point just before the mass on the rope is left to move freely, and the second point as the point just before the same mass falls onto the ground. Now, define the energy of the system (i.e. the sum of potential and kinetic energy) for point 1 and for point 2, and then set them equal.

KE=.5mv2 and PE=mgh

point 1 = PE
point 2 = KE + PE

so it would be mgh = .5mv2 + mgh
 
webdivx said:
KE=.5mv2 and PE=mgh

point 1 = PE
point 2 = KE + PE

so it would be mgh = .5mv2 + mgh

There is no potential energy at point 2, since the mass is alomst on the floor. Further on, '.5mv2' (which is supposed to be 0.5mv^2, I assume), as you wrote, is the kinetic energy of the mass attached to the rope. What is the kinetic energy of the cylinder? You have to count that energy in, too.
 
radou said:
There is no potential energy at point 2, since the mass is alomst on the floor. Further on, '.5mv2' (which is supposed to be 0.5mv^2, I assume), as you wrote, is the kinetic energy of the mass attached to the rope. What is the kinetic energy of the cylinder? You have to count that energy in, too.

is the kinetic energy of the cylinder .5mv^2 = .5MR^2
 
  • #10
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  • #11
Hootenanny said:
The total kinetic energy of the cylinder is the sum of the linear kinetic energy and the rotational kinetic energy of the cylinder. For more information on rotational kinetic energy, http://hyperphysics.phy-astr.gsu.edu/hbase/rke.html#rke"

:cry: i just don't understand. there's like a physics block in my mind. can somebody please solve for me.
 
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  • #12
webdivx said:
:cry: i just don't understand. there's like a physics block in my mind. can somebody please solve for me.
I'm afraid we won't solve it for you here; however, if you show some effort we will guide you through the problem. Now, the total energy of the system should be conserved, the pulley is frictionless so we can write the total energy of the pulley system as;

Total energy = Gravitation Potential Energy of mass + Kinetic Energy of the mass + rotational kinetic energy of the cylinder

Can you take the next step?
 

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