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Q. 64

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

Let’s examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: . Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S′ that is moving to the right at half the speed of light.

a. Use the Lorentz velocity transformation to find the velocity and the Newtonian momentum of A in S′.

b. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S′.

c. What is the total final momentum in S′?

d. Newtonian momentum was conserved in frame S. Is it conserved in frame S′?

a. the velocity in S' frame is

The momentum will be

b. the velocity of B in S' frame is and momentum

The velocity of C in S' frame is and momentum is

c. Total final momentum is

d. The momentum is not conserved.

See the step by step solution

Step by Step Solution

Part (a) Step 1: Given information

We have given,

Mass of A=

Mass of B =

Mass of C =

speed of B =

Speed of C =

We have to find the velocity and momentum of A in s' frame.

Step 2: Simplify

Using Lorentz's transformation, We can write

and momentum will be,

Part (B) Step 1: Given information

We have given,

Mass of B =

Speed of B=

Mass of C =

Speed of C=

We have to find the speed and momentum of B and C in s' frame.

Step 2: Simplify

Using Lorentz's transformation, We can write velocity of B is

and velocity of C is,

Now the momentum will be,

and momentum of C is,

Part (c) Step 1: Given information

We have find the final momentum in s' frame.

Step 2: Simplify

since,

Part (d) Step 1: Given information

We have to find that is momentum is conserved or not in s' frame.

Step 2: Simplify

Since, in S frame the total momentum is zero after decomposition.

But in S' frame it is not zero. then we can say that the momentum is not conserved in the S' frame.

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