In Fig. 37-28a, particle P is to move parallel to thex andx' axes of reference framesSand S', at a certain velocity relative to frame S. FrameS' is to move parallel to thex axis of frame Sat velocity v. Figure 37-28b gives the velocityu' of the particle relative to frameS' for a range of values forv . The vertical axis scale is set byu'a=0.800c . What value will u'have if (a) v=0.80cand (b)vc ?

Short Answer

Expert verified

(a) The value of u'is 2.5×108 m/s.

(b) The value of u'is3×108 m/s .

Step by step solution

01

Identification of given data

The given data can be listed below as:

  • The velocity of the frameS isv .
  • The velocity of the frame S'is u'.
  • The scale in the vertical axis is u'a=0.800c.
02

Significance of the reference frame

The reference frame is described as the position where the geometric points are being identified as physically and mathematically. This frame is set by some set of the reference points.

03

Determination of the value of u' if v=0.80c

(a)

According to the graph, whenv=0, then u=0.20c.

The equation of the velocity of the frameS'is expressed as:

u'=uv1uv/c2 …(i)

Here, u'is the velocity of the frame S', uis the initial and vis the final velocity of the frame. cis the speed of the light.

Substitute 0.20cfor role="math" localid="1663049487197" u, 3×108 m/sfor cand0.80c for vin the above equation.

u'=(3×108 m/s)(0.200.80)1+0.20×0.80=3×108 m/s1+0.16=3×108 m/s1.16=2.5×108 m/s

Thus, the value ofu' is 2.5×108 m/s.

04

Determination of the value of u' if  v→c

(b)

The equation (i) has been recalled below:

u'=uv1uv/c2

Substitute 0.20cfor u, 3×108 m/sfor cand 3×108 m/sfor vin the above equation.

u'=(3×108 m/s)(0.201)1+0.20=3.6×108 m/s1.20=3.6×108 m/s1.20=3×108 m/s

Thus, the value of u'is 3×108 m/s.

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