Answer to Question #86657 in Mechanics | Relativity for Ogooluwa

Question #86657
A body of mass 2500g is projected up an inclined plane with initial velocity 300cm3^-1. The plane is inclined at an angle 15° to the horizontal, and the coefficient of friction between the plane and the body is 0.25. determine how far up the plane it will go before coming to rest.
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Expert's answer
2019-03-20T11:47:47-0400

The Newton's second law states


ma=mgsinθμmgcosθma=-mg\sin\theta-\mu mg\cos\theta

The acceleration of a body

a=g(sinθ+μcosθ)=9.8(sin15+0.25cos15)a=-g(\sin\theta+\mu \cos\theta)=-9.8(\sin 15^{\circ}+0.25\cos 15^{\circ})

=4.9m/s2=-4.9\:\rm{m/s^2}

If the initial velocity is 10 m/s, the distance traveled by body before it will coming to rest

d=vi22a=(10m/s)22×(4.9)m/s2=10.2md=\frac{-v_i^2}{2a}=\frac{-(10\:\rm{m/s})^2}{2\times (-4.9)\:\rm{m/s^2}}=10.2\:\rm{m}


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