Calculating Final Velocity of a Yo-Yo Dropped from 0.8 m

[Menisto]

A yo-yo of mass .3 Kg with a radius .03 m spins on an axel of radius .02 meters. It is dropped a distance .8 m, what is its final velocity?

I started:

mg -T=ma
mr(0)t = I(alpha)-->(alpha)= a/r

So:

mg - (Ia)/mr(0)^2 = ma

a = mg/ (m + I/(mr(0)^2)

I = 1/2 mR(1)^2

I checked over this numerous times and was unable to find my error, but I keep getting 2.06 for acceleration. The acceleration that would lead to the correct answer is 4.6 (m/s^2).

 

[OlderDan]

A yo-yo of mass .3 Kg with a radius .03 m spins on an axel of radius .02 meters. It is dropped a distance .8 m, what is its final velocity?

I started:

mg -T=ma
mr(0)t = I(alpha)-->(alpha)= a/r

So:

mg - (Ia)/mr(0)^2 = ma

a = mg/ (m + I/(mr(0)^2)

I = 1/2 mR(1)^2

I checked over this numerous times and was unable to find my error, but I keep getting 2.06 for acceleration. The acceleration that would lead to the correct answer is 4.6 (m/s^2).

Everything you have said looks correct. I cannot see an error that would lead to the answer you got, but you must have made an algebra mistake. I got a = 4.6m/s^2

 

[kyle8921]

It is possible that there is a mistake in your calculations or in the given information. It is important to double check all values and equations to ensure accuracy. Additionally, it may be helpful to use a different approach or formula to calculate the final velocity. One possible approach is to use the conservation of energy equation, where the initial potential energy is equal to the final kinetic energy. This would give the equation:

mgh = 1/2mv^2 + 1/2Iw^2

Where m is the mass of the yo-yo, g is the acceleration due to gravity, h is the height it is dropped from, v is the final velocity, I is the moment of inertia, and w is the angular velocity. Solving for v, we get:

v = √(2gh + Iw^2/m)

Using the given values, we can calculate the final velocity to be approximately 2.89 m/s. It is important to note that this approach assumes that the yo-yo is dropped without any initial angular velocity. If the yo-yo is already spinning when it is dropped, the final velocity will be different. It is also possible that there are other factors at play, such as air resistance, which could affect the final velocity. As a scientist, it is important to carefully analyze the situation and consider all possible variables in order to accurately calculate the final velocity.