Pulley Mass Calculation: Atwood's Machine

[becca89]

Homework Statement

The two masses (m1 = 5.0 kg and m2 = 3.0 kg) in the Atwood's machine shown in Figure 10-23 are released from rest, with m1 at a height of 0.92 m above the floor. When m1 hits the ground its speed is 1.1 m/s. Assume that the pulley is a uniform disk with a radius of 12 cm.

Determine the pulley's mass.

Homework Equations

Conservation of Energy E_f=E_i
K= 1/2mv²+1/2Iw² (w = omega)
I = 1/2mr²

The Attempt at a Solution

I tried to cancel out as much as I could form the "K" equation and fill it in. Webassign keeps determining my answer wrong...

 

[Doc Al]

Show what you did. Hint: Don't forget gravitational potential energy.

 

[tomcue]

I would approach this problem by first identifying the known values and the unknown value. The known values are the masses of m1 and m2, the height of m1 above the ground, and the speed of m1 when it hits the ground. The unknown value is the mass of the pulley.

Next, I would use the conservation of energy equation, Ef=Ei, to solve for the unknown value. This equation states that the total energy of a system remains constant, so the initial energy (Ei) must equal the final energy (Ef).

The initial energy in this system is the potential energy of m1 at a height of 0.92 m above the ground, given by m1gh, where g is the acceleration due to gravity. The final energy is the kinetic energy of m1 just before it hits the ground, given by 1/2m1v^2.

Since the pulley is a uniform disk, we can use the moment of inertia equation, I=1/2mr^2, to calculate its moment of inertia. We know the radius of the pulley is 12 cm, so we can plug in this value and the unknown mass of the pulley into the equation.

Finally, we can set the initial energy equal to the final energy and solve for the unknown mass of the pulley. This will give us the correct answer for the pulley's mass.

It is possible that the answer you obtained using the above method was incorrect due to a calculation error. As a scientist, it is important to double check calculations to ensure accuracy. It is also possible that there was an error in the problem or in the software used for the homework assignment. In this case, it would be beneficial to reach out to the instructor for clarification or assistance.