Calculate the speed with which the light spot on the clouds moves.

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Homework Help Overview

The problem involves calculating the speed of a light spot on clouds caused by a laser mounted on a rotating turntable. The turntable rotates at 1200 revolutions per second, and the laser beam is angled at 30 degrees to the horizontal, with clouds located 50 km away.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using trigonometry to determine the radius of the circular path traced by the laser beam and the corresponding distance traveled. There are attempts to calculate the speed based on the distance and time taken for one revolution, leading to questions about the correctness of the calculations.

Discussion Status

Some participants are exploring different interpretations of the problem, particularly regarding the angular speed and its conversion from revolutions per second to radians per second. There is a recognition of the need to clarify the relationship between angular speed and the time for one revolution.

Contextual Notes

There is an ongoing discussion about the appropriate trigonometric functions to use based on the geometry of the situation, as well as confusion regarding the units of angular speed and its implications for the calculations.

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Homework Statement



A laser is placed on a turntable that rotates at 1200 rev/s. The laser, whose beam makes an angle of 30 degrees with the horizontal, shines on clouds 50km away. Calculate the speed with which the light spot on the clouds moves.

Homework Equations





The Attempt at a Solution



I guessed that you have to use trig to find the radius of the circle that the laser ends up "sweeping out", then find the circumference, then find the speed..since speed = dist/time (and t = 2pi/w)..but it doesn't come to the right answer (3.3 x 10^8 m/s), so where am i going wrong?

Thanks!
 
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Your method sounds good to me. Show the details of your calculation.
 


Well, using simple trig, i get the radius of the circle to be 50000tan60 meters. therefore the total dist. traveled is 2 pi (50000tan60)..

and the time taken is 2pi/1200

but when you divide the distance by the time, it doesn't give you the right speed (which should be around 3.3 x 10^8...

any ideas?
 


bon said:
Well, using simple trig, i get the radius of the circle to be 50000tan60 meters.
The distance given is the distance to the cloud. You want the horizontal component of that distance.
 


ok so 50000sin60..it still doesn't give me the right answer..
 


bon said:
ok so 50000sin60..it still doesn't give me the right answer..
It does for me. Show the steps in your calculation.
 


dist = 50000sin60 x 2pi

time = 2pi/1200 s

dist / time =/= 3.3 x 10^8
 


bon said:
dist = 50000sin60 x 2pi
Right. The distance for one revolution.
time = 2pi/1200 s
Not right. Note that the angular speed is given in rev/sec, not rad/sec.
 


Doc Al said:
Right. The distance for one revolution.

Not right. Note that the angular speed is given in rev/sec, not rad/sec.

Ah ok great. Thanks for your help.

so angular speed is in rev/sec...what the w then in: T = 2pi/w...

please could you explain the difference..
thanks
 
  • #10


Well, if the angular speed is 1200 revs/sec, then 1 rev takes 1/1200 sec.

The relationship T = 2pi/ω is only valid if ω is in rad/sec. 1200 rev/sec = 1200*2pi rad/sec.
So: T = 2pi/ω = 2pi/(1200*2pi) = 1/1200 sec.
 

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