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Chapter 6: Q50P (page 1250)

The net force F鈫�on a particle of mass m is directed at 30.0掳counter-clockwise from the +x - axis. At one instant of time, the particle is travelling in the +x - direction with a speed (measured relative to the earth) of 0.700c . At this instant, what is the direction of the particle鈥檚 acceleration?

Short Answer

Expert verified

The direction of the particle鈥檚 acceleration is at48.5掳 counter clockwise from the +x - axis.

Step by step solution

01

Given data

Speed of the particle v=0.700c

Force on a particle of mass m is directed 胃F=30.0掳

02

Define the acceleration.

The rate of change of velocity with respect to time is known as acceleration.

a鈫�=dvdt

The force of particle is F = ma .

From the above figure:

Fll=y3mallF鈯�=yma鈯�F鈯�Fll=a鈯�y2alla鈯�all=y2F鈯�Fll

03

Determine the direction particle’s acceleration.

From the figure (a):

Fll=Fcos胃FF鈯�=Fsin胃f

And from the figure (b):

all=acos胃aa鈯�=asin胃a

So,asin胃aacos胃a=Fcos胃F1-v2/c2Fsin胃F

Where, is speed of particle and纬=1/1-v2/c2

Now,胃a=tan-1tan胃1-v2/c2=tan-1tan胃1-0.7002=48.5掳

Hence, the direction of the particle鈥檚 acceleration is at48.5掳 counter clockwise from the +x - axis.

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