Conservation of energy and string pulley problem

In summary, given two masses of 3.3 kg and 7.4 kg connected by a string passing over a pulley with a moment of inertia of 12 g · m2, and released from rest with the system not slipping, the linear speed of the masses after the 7.4 kg mass descends 21 cm can be found by using the equations for change in potential energy and kinetic energy. However, if the moment of inertia is given in grams rather than kilograms, the resulting calculation will not yield the correct answer.
  • #1
gunster
7
0

Homework Statement


Consider two masses of 3.3 kg and 7.4 kg
connected by a string passing over a pulley
having a moment of inertia 12 g · m2
about its axis of rotation, as in the figure below. The
string does not slip on the pulley, and the
system is released from rest. The radius of
the pulley is 0.35 m.

Find the linear speed of the masses after
the 7.4 kg mass descends through a distance
21 cm. Assume mechanical energy is conserved during the motion. The acceleration of
gravity is 9.8 m/s^2.

Answer in units of m/s

Homework Equations



delta PE = KE
KE = K(translational) + K(rotational)

The Attempt at a Solution



Found that change in potential energy should be equal to change in potential energy of the heavier mass (where PE is lost) subtracted by the change in potential energy of the lighter mass (where some PE is gained).

Therefore: 7.4*g*(21/100) - 3.3 * g * (21/100) = delta PE

I then set total change in KE to the delta PE. I determined rotational KE to be 1/2 I * omega^2

where I is given to me and omega is (v/r)^2 and r is given to me.

K translational = 1/2 * Mtotal * v^2. I factored out V^2, and set that equal to delta PE / rest of that mess

So in the end: v = sqrt ( delta PE / (6/r^2 + 1/2M)).

However, it wasn't the right answer :( so any ideas?
 
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  • #2
In what units is the moment of inertia given?
 
  • #3
wow I see the moment of inertia is given in grams. Thank you so much that would explain why I failed XD
 

FAQ: Conservation of energy and string pulley problem

What is the conservation of energy and how does it relate to a string pulley problem?

The conservation of energy is a fundamental law in physics that states energy cannot be created or destroyed, only transferred or transformed. In a string pulley problem, energy is conserved as the amount of energy put into the system at the beginning is equal to the amount of energy output at the end.

How do you calculate the potential and kinetic energy in a string pulley system?

To calculate potential energy, you need to know the height and mass of the object in the system. The formula is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. To calculate kinetic energy, you need to know the mass and velocity of the object. The formula is KE = 1/2mv^2, where m is the mass and v is the velocity.

Can you explain the concept of mechanical advantage in relation to a string pulley system?

Mechanical advantage is the measure of the amplification of force achieved by using a machine, in this case, a string pulley system. The more pulleys in the system, the greater the mechanical advantage and the easier it is to lift a heavy object with less force.

How does friction affect the conservation of energy in a string pulley problem?

Friction is a force that opposes motion and can cause energy to be lost in a string pulley problem. Some of the energy put into the system is converted into heat due to the friction between the pulley and the string. This means that the output energy at the end will be slightly less than the input energy.

What are some real-world applications of the conservation of energy and string pulley problems?

The conservation of energy and string pulley problems are used in various real-world applications, such as elevators, cranes, and simple machines like a bicycle. These concepts are also used in engineering and construction to design efficient and effective systems for lifting heavy objects. In addition, understanding the conservation of energy is crucial in understanding energy sources and their impact on the environment.

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