Solving for Time in Uniform Circular Motion and Moving Sidewalk Problems

[shade585]

Homework Statement

A centripetal-acceleration addict rides in uniform circular motion with period T = 3.58 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2)i + (-6.00 m/s2)j. At that instant, what are the following values?

I found r x a to be 0 m^2/s^2 which is right. I cannot figure out v dot a.

Homework Equations

I used the Period equation to get a velocity of 5.27 m/s.

The Attempt at a Solution

From here I do not know what to do.

Homework Statement

The airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk. He takes 185 s to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in 108 s. Moe boards the sidewalk and walks along it. How long does Moe take to move through the corridor? Assume that Larry and Moe walk at the same speed.

Homework Equations

I know the distance to be the same. I know i have two velocities. One is the velocity at which Larry and Moe walk. The other is the velocity of the sidewalk. I set up the distance to be a ratio of the distance over the time it took to go the length of the sidewalk. I cannot figure out how to make d cancel out. I know that i need to find an algebraic equation that will do so. I think i just need a nudge in the right direction.

 

[FedEx]

Homework Statement

A centripetal-acceleration addict rides in uniform circular motion with period T = 3.58 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2)i + (-6.00 m/s2)j. At that instant, what are the following values?

I found r x a to be 0 m^2/s^2 which is right. I cannot figure out v dot a.

Homework Equations

I used the Period equation to get a velocity of 5.27 m/s.

The Attempt at a Solution

From here I do not know what to do.

Homework Statement

The airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk. He takes 185 s to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in 108 s. Moe boards the sidewalk and walks along it. How long does Moe take to move through the corridor? Assume that Larry and Moe walk at the same speed.

Homework Equations

I know the distance to be the same. I know i have two velocities. One is the velocity at which Larry and Moe walk. The other is the velocity of the sidewalk. I set up the distance to be a ratio of the distance over the time it took to go the length of the sidewalk. I cannot figure out how to make d cancel out. I know that i need to find an algebraic equation that will do so. I think i just need a nudge in the right direction.

What is the formula of centripetal acceleration?

 

[shade585]

a = v^2/r

 

[FedEx]

a = v^2/r

Oh sorry.You are just told to find out a dot b.So in that case angle between a and v is 90 and hence a dot b is 0. I hope that i have not misunderstood your question.

 

[shade585]

Oh ok. I see it now. Thanks for the help.

 

[CompuChip]

As for the second question, suppose that the length of the sidewalk is d m. Then Larry's velocity is $v_L = d / 185$ m/s and the velocity of the sidewalk is $v_S = d / 108$ m/s.
Now what is Moe's velocity? Once you have the velocity, how can you find the time it takes him to walk d m?

Now tell us: is the problem in writing down this equation or in solving it?

 

[shade585]

i had the two velocities. Moe's velocity should be d/185 m/s + d/108 m/s. The equation I can think of is d = (d/185 m/s + d/108 m/s)t.

 

[CompuChip]

That's correct, so the problem is in solving for t.
You have an equation of the form
$$d = \left( \frac{d}{a} + \frac{d}{b} \right) t.$$
Try writing the bracketed term in one fraction,
$$\frac{d}{a} + \frac{d}{b} = \frac{db}{ab} + \frac{da}{ab} = \frac{d(a + b)}{a b}.$$
Now can you solve it?

 

[shade585]

yes thank you. it seems so obvious now. I got 68 seconds.

 

[CompuChip]

I got that too (actually, $68 \frac{56}{293}$), but usually an error of one significant digit is allowed (technically speaking, all numbers in the question are given in three significant digits, so if you want to write your answer decimally you would write it with the same precision, e.g. 68,2 s)