Uniform circular motion merry-go-round

[Jadalucas]

Homework Statement

A purse at radius 1.90 m and a wallet at radius 2.60 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (1.70 m/s2) + (4.60 m/s2). At that instant and in unit-vector notation, what is the acceleration of the wallet?

Homework Equations

Tan(theta)= -(V^2/r)sin(theta)/-(V^2/r)Cos(theta)
A=V^2/r
T(period)=2pir/v

The Attempt at a Solution

I used the original components of the purse to determine the angle created from the acceleration components
1) Tan(theta)= (4.6m/s^2)/(1.70m/s^2)
Arc Tangent (4.6/1.7)=theta and I found theta=69.72 degrees

next, I used the angle to determine the new components of the wallet using the same velocity but at a different radius (2.6m)

2) 2.6 Cos69.72= acceleration of wallet about x = .901m/s^2
2.6 sin69.72 = acceleration of wallet about y = 2.44m/s^2

-I put those components into the unite vector notation and got the problem wrong... I'm wondering why, if anyone could please help. thanks

 

[kuruman]

Homework Statement

A purse at radius 1.90 m and a wallet at radius 2.60 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (1.70 m/s2) + (4.60 m/s2). At that instant and in unit-vector notation, what is the acceleration of the wallet?

Are there unit vectors multiplying these components? If so, what are they?

 

[Jadalucas]

the only unit vectors that had been provided were the acceleration of the purse is (1.70 m/s2)i + (4.60 m/s2)j *apparently those letters didn't show up in the earlier post.

 

[kuruman]

the only unit vectors that had been provided were the acceleration of the purse is (1.70 m/s2)i + (4.60 m/s2)j *apparently those letters didn't show up in the earlier post.

Can you find the magnitude of the acceleration of the purse?
Once you have that, can you find the magnitude of the acceleration of the wallet?
Once you have that, can you find the components of the acceleration of the wallet?

Hint: The wallet's acceleration vector is proportional to the purse's acceleration vector. What is the constant of proportionality?

 

[paranormal]

Your approach seems correct, but there may be a slight error in your calculations for the x and y components of the wallet's acceleration. Remember that the acceleration of the wallet is still in the same direction as the purse's acceleration, just with different magnitudes due to the different radii. So, the x component of the wallet's acceleration should also be 1.70 m/s^2, since it is still in the same direction as the purse's acceleration in the x direction. Similarly, the y component of the wallet's acceleration should be 4.60 m/s^2, since it is still in the same direction as the purse's acceleration in the y direction.

Therefore, in unit vector notation, the acceleration of the wallet would be (1.70 m/s^2)i + (4.60 m/s^2)j.

It's also important to note that the angle theta that you calculated is the angle between the purse's acceleration and the radial line connecting the center of the merry-go-round to the purse. This angle is not necessarily the same as the angle between the radial line and the wallet's acceleration. In this case, the angle between the radial line and the wallet's acceleration would be 90 degrees minus theta, since the purse and wallet are on the same radial line.

I hope this helps clarify things for you. Keep up the good work!