Question

5.) A 1000kg The coefficient of friction is .2 How far does the car travel uphill before it comes to rest? car travelling at 20m/s encounters a 200 incline. Distance- booka

Answer 1

from the free body diagram we have

in y direction we have

Fy=ma_y

Fn-mgcos$\Theta$=0

so Fn=mgcos$\Theta$...........1)

and Fr=$\mu$Fn

so using eqn 1 we have

Fr=$\mu$mgcos$\Theta$........2)

we have the formula for kinetic energy

K.E=1/2mv²

and the work done by the friction force is

Fr*d=$\mu$mgcos$\Theta$*d

when the block reaches the top, the kinetic energy changes to potential energy

so P.E=mgh=mgsin$\Theta$*d

P.E=K.E-work done by friction

mgsin$\Theta$*d=1/2mv²-$\mu$mgcos$\Theta$*d

gsin$\Theta$*d=1/2v²-$\mu$gcos$\Theta$*d

1/2v²=d(gsin$\Theta$+$\mu$gcos$\Theta$)

1/2*20²=d(9.8*sin20^o+0.2*9.8*cos20^o)

200=d(5.1936)

d=200/5.1936=38.5m

so answer is 38.5m

PrD 74 f n