Meter Stick Special Relativity Problem

AI Thread Summary
The problem involves a meter stick at a 30° angle in frame S' moving at 0.82c relative to frame S, requiring the calculation of its length in frame S. The length contraction formula L=Lo/γ is applied, with γ calculated as 1.747 and Lo as 1m, resulting in an initial contracted length of 0.572m. To accurately find the length in frame S, the x and y components of the stick must be calculated separately, as only the x-component will undergo contraction. The correct approach involves using the Pythagorean theorem after determining the contracted x-component and the unchanged y-component. The discussion emphasizes the importance of separating components for accurate length measurement in different frames.
harrietstowe
Messages
46
Reaction score
0

Homework Statement



A meter stick in frame S' makes an angle of 30° with the x' axis. If that frame moves parallel to the x-axis with speed 0.82c relative to frame S, what is the length of the stick as measured from S?

Homework Equations



Length contraction: L=Lo/γ

The Attempt at a Solution


Relative to s, the length of this meter stick will contract. γ=1.747
Lo = 1m
L = .572
I then multiplied this by the cosine of 30 degrees to get .088 m but this is not the right answer. Multiplying by the cosine of 30 degrees was sort of a guess as I am unsure of what to do with it.
Thanks

Thanks
 
Physics news on Phys.org
harrietstowe said:
Relative to s, the length of this meter stick will contract. γ=1.747
Lo = 1m
L = .572
I then multiplied this by the cosine of 30 degrees to get .088 m but this is not the right answer. Multiplying by the cosine of 30 degrees was sort of a guess as I am unsure of what to do with it.
Work with the x-component and y-component separately. Calculate the x-component and the y-component of the meter stick in its own frame of reference (the S' frame). Only the x-component will contract in the S frame. Then use the Pythagorean theorem to find the total length (in the S frame) after contraction. :wink:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Length Contraction: Sally & Sheldon's Meter Stick
Replies
11
Views
2K
Angled falling Meter Stick on a frictionless surface
Replies
14
Views
2K
I How many meter sticks are there in this length contraction reasoning?
Replies
12
Views
2K
Special Relativity Muon problem
Replies
6
Views
2K
Length of a Wave Train in Special Relativity
Replies
13
Views
2K
How Does Relativity Affect the Motion of a Falling Stick?
Replies
1
Views
1K
Solving Special Relativity Problem with Train Walking
Replies
14
Views
3K
Length contraction and Time dilation for LIGHT?
Replies
8
Views
2K
How Does Special Relativity Affect the Angle of a Meter Stick in a Moving Frame?
Replies
5
Views
8K
Special relativity - measure of a rod and simultaneity
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top