an objet of mass m is at rest at the top of a smooth slope of height h and lengt

Question

an objet of mass m is at rest at the top of a smooth slope of height h and length L,the coiffecient of kinetic friction between the object and the surface mk is small enough that the object will slide down the slope if a given a very small push to get it started,find an expression for the object speed at the bottom of the slope an objet of mass m is at rest at the top of a smooth slope of height h and length L,the coiffecient of kinetic friction between the object and the surface mk is small enough that the object will slide down the slope if a given a very small push to get it started,find an expression for the object speed at the bottom of the slope an objet of mass m is at rest at the top of a smooth slope of height h and length L,the coiffecient of kinetic friction between the object and the surface mk is small enough that the object will slide down the slope if a given a very small push to get it started,find an expression for the object speed at the bottom of the slope

Explanation / Answer

Given,

height=h

length=L

let mass be m.

so if the slope makes angle theta with horizontal then

sin(theta)=h/L

normal force=m*g*cos(theta)

the gravitational force down the incline=m*g*sin(theta)

friction force=k*m*g*cos(theta)

the net force down the incline=m*g*(sin(theta)-k*cos(theta))

acceleration=g*(sin(theta)-k*cos(theta))

velocity after covering distance L=sqrt(2*acceleration*distance)=sqrt(2*g*(sin(theta)-k*cos(theta))*L)

where sin(theta)=h/L

cos(theta)=sqrt(L^2-h^2)/L

an expression for the object speed at the bottom of the slope is cos(theta)=sqrt(L^2-h^2)/L

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