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

In summary, the problem involves finding the speed of a laser on a rotating turntable as it shines on a cloud 50km away. Using trigonometry, the horizontal component of the distance is calculated to be 50000sin60 meters. The correct calculation for time should be 2pi/1200 seconds, as the angular speed is given in revolutions per second. This results in a speed of approximately 3.3 x 10^8 m/s, which matches the expected answer.
  • #1
bon
559
0
Special Relativity URGENT!

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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  • #2


Your method sounds good to me. Show the details of your calculation.
 
  • #3


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?
 
  • #4


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.
 
  • #5


ok so 50000sin60..it still doesn't give me the right answer..
 
  • #6


bon said:
ok so 50000sin60..it still doesn't give me the right answer..
It does for me. Show the steps in your calculation.
 
  • #7


dist = 50000sin60 x 2pi

time = 2pi/1200 s

dist / time =/= 3.3 x 10^8
 
  • #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.
 
  • #9


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.
 

1. How do you calculate the speed of the light spot on the clouds?

To calculate the speed of the light spot on the clouds, you will need to measure the distance between two points on the clouds and the time it takes for the light spot to move between those two points. Then, divide the distance by the time to get the speed in meters per second.

2. What equipment is needed to measure the speed of the light spot on the clouds?

You will need a stopwatch or timer to measure the time it takes for the light spot to move between two points on the clouds. You may also need a ruler or measuring tape to measure the distance between those two points.

3. What factors can affect the accuracy of the calculated speed of the light spot on the clouds?

Some factors that can affect the accuracy of the calculated speed include human error in measuring the distance or time, wind or other weather conditions that may affect the movement of the light spot, and the angle at which the light spot is being observed from.

4. Can the speed of the light spot on the clouds change over time?

Yes, the speed of the light spot on the clouds can change over time. Factors such as wind speed and direction, cloud movement, and the position of the light source can all affect the speed of the light spot.

5. How can knowing the speed of the light spot on the clouds be useful?

Knowing the speed of the light spot on the clouds can be useful for studying atmospheric conditions and patterns, as well as for predicting weather events. It can also help in understanding the movement of clouds and how they may impact the amount of sunlight reaching the Earth's surface.

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