Work Energy Theorem and Uniform Disc Problem

[theBEAST]

Homework Statement

Using work energy theorem, solve:

The Attempt at a Solution

The actual answer (3.11s) is exactly half of my answer. Does anyone know what I did wrong?

 

[grzz]

Note that moment of inertia of a uniform disc about an axis through its centre and perpendicular to its plane is

$\frac{1}{2}$MR$^{2}$.

 

[theBEAST]

Note that moment of inertia of a uniform disc about an axis through its centre and perpendicular to its plane is

$\frac{1}{2}$MR$^{2}$.

Yup! That is what I used I believe.

 

[haruspex]

Yup! That is what I used I believe.

There should be two factors of 1/2 - one from Iω²/2 for the KE and another from I=Mr²/2.

 

[Nickie]

I would like to first clarify that the Work Energy Theorem states that the work done on an object is equal to the change in its kinetic energy. In the context of the Uniform Disc Problem, this means that the work done by the applied force (in this case, the friction force) is equal to the change in kinetic energy of the disc.

To solve this problem, we can use the formula for work done: W = Fd, where W is the work done, F is the applied force, and d is the distance over which the force is applied. In this case, the distance is the circumference of the disc, which is 2πr, where r is the radius of the disc.

Therefore, the work done by the friction force can be written as W = μmg(2πr), where μ is the coefficient of friction, m is the mass of the disc, and g is the acceleration due to gravity.

According to the Work Energy Theorem, this work done by the friction force is equal to the change in kinetic energy of the disc, which can be written as ΔKE = ½mv^2 - 0, since the disc starts from rest. So, we can equate these two equations and solve for v, which gives us v = √(2μgr).

Now, to find the time it takes for the disc to stop, we can use the formula for velocity: v = d/t, where d is the distance traveled and t is the time taken. In this case, the distance traveled is the circumference of the disc, which is 2πr, and the final velocity is 0, since the disc stops. So, we can write the equation as 0 = (2πr)/t, which gives us t = (2πr)/v.

Substituting the value of v we found earlier, we get t = (2πr)/√(2μgr). Plugging in the given values of μ, m, and r, we get t = (2π*0.2*0.5)/(√(2*9.8*0.5)) = 3.11 seconds.

Therefore, the time it takes for the disc to stop is 3.11 seconds, which is the correct answer. It is possible that you made a calculation error or used incorrect values, which led to your answer being different. I