It is about finding kinetic energy want help in part 1 not part 2 in part 1 please tell how to find velocity?

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1 Answer
A08
Apr 28, 2018

(i) Driving Force of the engine #="Wattage"/"velocity"#
At the bottom of hill
Net force upwards #=30000/v_"bottom"-1000-mgsin theta#
#g# is acceleration due to gravity and #theta# is the angle of the incline.
#=>#Net force upwards #=30000/v_"bottom"-1000-1250xx9.81xx30/500#
Using Newton's Second Law of motion

This must be #="Mass of car" xxa_"bottom"=1250xx4#

Therefore we get

#30000/v_"bottom"-1000-735.75=5000#
#=>30000/v_"bottom"=6735.75#
#=>v_"bottom"=4.45\ ms^-1#, rounded to two decimal places

Similarly for #v_"top"#

#30000/v_"top"-1000-735.75=1250xx0.2#
#=>v_"top"=15.11\ ms^-1#, rounded to two decimal places

Gain in KE#=1/2xx1250(v_"top"^2-v_"bottom"^2)#

(ii) Work Done by car’s engine

#=\ "Gain in KE" + "Gain in PE" + "Work Done against resistance"#

  1. #"Gain in KE"# from part (i)
  2. #"Gain in PE"\ =mgh=1250xx9.81xx30=367875\ J#
  3. #"Work Done against resistance"="resistance"xx"distance"#
    #=1000xx500=500000\ J#

(I have used #g=9.81\ ms^-2#. In some text books show a value of #g=10ms^-2#) Choose value of your liking.

Hope this helps.

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