1. ## Newtonian Mechanics

A block of mass m is given an initial velocity of u0 at a fixed origin O and it began toslide on a rough horizontal surface. At a position x from O, it has a velocity of v. Takethe magnitude of the acceleration due to gravity to be g and the coefficient of slidingfriction to be μ. (a) Apply Newtonian mechanics and present the equation of motion for the block. the answer i got was a=μg. anyone out there could confirm if i am right? or help me if i am wrong

2. ## Re: Newtonian Mechanics

$|a| = \mu g$ ... you've stated the magnitude of acceleration.

kinetic friction acts opposite to the direction of motion ...

$a= \dfrac{F_{net}}{m} = \dfrac{-\mu mg}{m} = -\mu g$

$v = u_0 - \mu g t$

also, the work/kinetic energy theorem yields an equation of motion without the parameter of time ...

$W_{net} = -f \cdot x = \Delta KE = \dfrac{1}{2}mv^2 - \dfrac{1}{2}m u_0^2$

$-\mu mg x = \dfrac{1}{2}m(v^2-u_0^2)$

$v^2 = u_0^2 - 2\mu g x$

3. ## Re: Newtonian Mechanics

i see. thanks for the clarification