Understanding Mechanics and Relativity: Two Problems and Their Solutions

AI Thread Summary
A spaceship traveling at 0.8c shoots a laser pulse backward at 3 x 10^8 m/s, prompting a question about the speed of the laser as measured from Earth. According to the principles of relativity, the speed of light remains constant at c in all inertial frames, meaning the calculation of the laser's speed cannot simply be 0.8c - 3 x 10^8. In a separate problem involving two blocks on an incline, the discussion centers on analyzing forces and understanding Newton's third law, particularly in a dynamic equilibrium scenario. The tension in the ropes connecting the blocks must be considered, as they may not be equal, leading to different equations for each block. Clarification on these concepts is essential for solving both problems accurately.
Pseudo Statistic
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I'm having 2 problems... with two questions...

1) A spaceship travels with a constant speed 0.8c as it passes over Earth; some time after passint Earth, the pilor shoots a laser pulse backward at a speed of 3 x 10^8 meters per second with respect to the spaceship. Determine the speed of the laser pulse as measured by a person on Earth.

What does relativity say about stuff like this involving things traveling at the speed of light? Would it be 0.8 c - 3 x 10 ^8? Or is that incorrect?

2) There's a question with a diagram like this:
http://www.brokendream.net/xh4/diagphys2.jpg
Blocks 1 and 2 of masses m1 and m2 respectively are connected by a light string, as shown above. These blocks are further connected to a block of mass M by another light string that passes over a pulley of negligible mass and friction. Blocks 1 and 2 move with a constant velocity v down the inclined plane, which makes an angle theta with the horizontal. The kinetic frictional force on block 1 is f and that on block 2 is 2f.

Normally I know how to do these questions but I'm having one little problem- how do I analyze the forces on m1 and m2? I mean, since they're moving down the incline at constant velocity, they're in dynamic equilibrium which means the sum of all forces = 0 and in m2's case I'm thinking the forces would be:
m2 g sin theta - 2f - T = 0 ? And on m1, m1 g sin theta - f = 0 and T - Mg = 0? But does m1 or m2 exert a force on the other or something?
I don't know, I guess I never really understood Newton's third law...

Can someone please clarify? Thanks a lot.
 
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Pseudo Statistic said:
I'm having 2 problems... with two questions...

1) A spaceship travels with a constant speed 0.8c as it passes over Earth; some time after passint Earth, the pilor shoots a laser pulse backward at a speed of 3 x 10^8 meters per second with respect to the spaceship. Determine the speed of the laser pulse as measured by a person on Earth.

What does relativity say about stuff like this involving things traveling at the speed of light? Would it be 0.8 c - 3 x 10 ^8? Or is that incorrect?
.

What is the fundamental principle of special relativity? That in *any* inertial frame the speed of light is always equal to c, no?

Pat
 
Pseudo Statistic said:
2) There's a question with a diagram like this:
http://www.brokendream.net/xh4/diagphys2.jpg
Blocks 1 and 2 of masses m1 and m2 respectively are connected by a light string, as shown above. These blocks are further connected to a block of mass M by another light string that passes over a pulley of negligible mass and friction. Blocks 1 and 2 move with a constant velocity v down the inclined plane, which makes an angle theta with the horizontal. The kinetic frictional force on block 1 is f and that on block 2 is 2f.

Normally I know how to do these questions but I'm having one little problem- how do I analyze the forces on m1 and m2? I mean, since they're moving down the incline at constant velocity, they're in dynamic equilibrium which means the sum of all forces = 0 and in m2's case I'm thinking the forces would be:
m2 g sin theta - 2f - T = 0 ? And on m1, m1 g sin theta - f = 0 and T - Mg = 0? But does m1 or m2 exert a force on the other or something?
I don't know, I guess I never really understood Newton's third law...

Can someone please clarify? Thanks a lot.

There are *two* ropes in the problem and the tension in each rope is not (necessarily) the same. Your equation for m2 should be m2 g sin theta - 2f - T_1 +T_2 = 0 and so on.
 
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nrqed said:
What is the fundamental principle of special relativity? That in *any* inertial frame the speed of light is always equal to c, no?

Pat
So the answer is 3 x 10^8 in this case?
 
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