A particle is sliding down along an inclined plane. Frictional force is 0.2 times the normal reaction , and the inclination of the plane is `60^@` . What is the acceleration of the particle ? If the mass of the particle is 1g , find the change in the sum of potential and kinetic energies of the particle as it slides down the plane by 1 m.

Explanation

Let the acceleration of the particle along inclined plane =a and the downward force on the particle along the plane = `mg sin theta -f ` [Fig.1.25].

`therefore ma =mg sin theta -mu R =mg sin theta -mumg cos theta`
` or, a=g (sin theta -mu cos theta)=9.8 (sin 60^@ -0.2 cos 60^@)`
`=9.8 (sqrt(3)/2-0.2xx1/2)=7.5 m*s^(-2)`
Change in mechanical energy =work done against friction
`mu mg cos theta *s`
`=0.2 xx0.001 xx9.8xx1/2 xx1=0.00098 J`.