Question #39b14
1 Answer
(a) Given street incline
Let Distance moved by Chemistro along the street
Total energy of Chemistro at any instant of time
#=mgh+1/2mv^2#
Where#m# is mass of Chemistro and#g=10ms^-2# acceleration due to gravity
Initial total energy
Initial kinetic energy gets converted in
Final total energy when he comes to rest
Now work done by friction
From the figure we see that the normal reaction
#N = mgcos20^@#
therefore force of the sliding friction is
#F_f= μ_kN = μ_kmgcos20^@#
#:.W=-μ_kmgcos20^@xxl#
As force of friction and distance moved are opposite to each other we have#-ve# sign.
Inserting given values and using law of conservation of energy we get
#21780=900lsin 20^@+0.333xx90.0xx10lcos20^@#
#=>21780=900lxx0.3420+0.333xx90.0xx10lxx0.9397#
#=>21780=(307.8+281.6)l#
#=>l=37.0m# , three significant figures
#:.h=36.95xxsin20^@#
#=>h=12.6m#
(b) Heat generated by sliding is same as work done against friction
#=0.333xx90.0xx10xxlcos20^@#
#=0.333xx90.0xx10xx36.95xx0.9397=10406J#
(c) We know that power is the rate of doing work per unit time.
#:.# Average power delivered by Power Man#=21780/0.300# #=72600Js^-1#