Conservation of Energy with kinematics

In summary, the problem involves finding the speed of a block after it has descended 50 cm from rest, using energy conservation principles. In part (a), R = 12 cm, M = 570 g, and m = 50 g, while in part (b), R = 5.0 cm. The block hangs from a massless cord wrapped around the rim of a mounted uniform disk, with no slipping or friction at the axle. The equations used include force = mass x acceleration, torque = moment of inertia x angular acceleration, and conservation of energy (U + K = U + K). To solve the problem, the equations for kinetic energies and moment of inertia should be checked, and the linear velocity should be substituted
  • #1
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Homework Statement



(a) If R = 12 cm, M = 570 g, and m = 50 g in Figure 10-18 (below), find the speed of the block after it has descended 50 cm starting from rest. Solve the problem using energy conservation principles.

M is the mass of the mounted uniform disk.
A block with mass m hangs from a massless cord that is wrapped around the rim of the disk. The cord does not slip, and there is no friction at the axle.(b) Repeat (a) with R = 5.0 cm.

Homework Equations



F = ma
alpha * R = a

torque = I * alpha

U+K = U+K

The Attempt at a Solution

I understood how to solve this problem (#9) with kinematics ( solving for acceleration and then using v^2 = vnot^2 + 2ad) but am having trouble with using conservation of energy.This was my attempt

U + K = U + K
//It is initially at rest
0 + 0 = -mgh + Krotational + Ktangential

mgh = 05*I*omega + 0.5mv

I = 0.5mr = .004104 kg * m

a = 1.4626 so alpha = 12.189 rad/s

I don't think my initial setup is correct though because I do not get the correct answer
If someone could show me how I can post the image up here that'd be great too
Thanks!
 
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  • #2
Check the equations for the kinetic energies and moment of inertia. ehild
 
  • #3
A few things to get you started:
joej24 said:
mgh = 05*I*omega + 0.5mv
I think you mean
mgh = ½2 + ½mv2

I'm guessing you just made a typo.
a = 1.4626 so alpha = 12.189 rad/s
There's no point in solving for the linear acceleration or the angular acceleration, when using conservation of energy for this problem.

All you need to do is solve for the velocity. You'll notice that there is an ω in your conservation of energy equation. Given the way the setup is described, with a cord wrapped around the rim of the disk, there is a very simple relationship between the linear velocity v and the angular velocity ω. Make the appropriate substitution of ω in terms of v. Then simply solve for v.
bump
Per the forum rules we can't help you unless you show that you've put an effort into solving the problem. You mentioned, "I don't think my initial setup is correct though because I do not get the correct answer." So, ... show us your work, and how you got to an answer. :smile:
 

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another.

2. How does the law of conservation of energy apply to kinematics?

In kinematics, the law of conservation of energy means that the total energy of a system remains constant, even as the kinetic and potential energy of the objects within the system may change.

3. What are some examples of the conservation of energy in kinematics?

Examples of the conservation of energy in kinematics include a roller coaster, where potential energy is converted into kinetic energy as the car moves downhill, and a pendulum, where potential energy is converted into kinetic energy as the pendulum swings back and forth.

4. How can we calculate the conservation of energy in kinematics?

The conservation of energy in kinematics can be calculated using the equation E = KE + PE, where E represents total energy, KE represents kinetic energy, and PE represents potential energy. By plugging in the values for KE and PE at different points in the system, we can determine if the total energy remains constant.

5. What happens if the law of conservation of energy is violated in kinematics?

If the law of conservation of energy is violated in kinematics, it means that energy is being created or destroyed within the system. This is not possible according to the laws of physics, and it may indicate that there are external forces or factors at play that need to be considered in the analysis of the system.

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