Answer:(a)891.64 N
(b)0.7
Explanation:
Mass of crate [tex]m=100 kg[/tex]
Crate slows down in [tex]s=1.5 m[/tex]
initial speed [tex]u=1.77 m/s[/tex]
inclination [tex]\theta =30^{\circ}[/tex]
From Work-Energy Principle
Work done by all the Forces is equal to change in Kinetic Energy
[tex]W_{friction}+W_{gravity}=\frac{1}{2}mv_i^2-\frac{1}{2}mv_f^2[/tex]
[tex]W_{gravity}=mg(0-h)=mgs\sin \theta [/tex]
[tex]W_{gravity}=-mgs\sin \theta[/tex]
[tex]W_{gravity}=-100\times 9.8\times 1.5\sin 30=-735 N[/tex]
change in kinetic energy[tex]=\frac{1}{2}\times 100\times 1.77^2=156.64 J[/tex]
[tex]W_{friction}=156.64+735=891.645[/tex]
(b)Coefficient of sliding friction
[tex]f_r\cdot s=W_{friciton}[/tex]
[tex]891.645=f_r\times 1.5[/tex]
[tex]f_r=594.43 N[/tex]
and [tex]f_r=\mu mg\cos \theta [/tex]
[tex]\mu 100\times 9.8\times \cos 30=594.43[/tex]
[tex]\mu =0.7[/tex]
