Let the object go. On a frictionless slope the only force along the surface is $mg\sin\theta$, and Newton says $ma = mg\sin\theta$. Divide both sides by $m$ and it is gone: $a = g\sin\theta$, a equals g sin theta, where $a$ is the down-slope acceleration in $\mathrm{m/s^2}$, $g = 9.8\ \mathrm{m/s^2}$, and $\theta$ is the slope above the horizontal. A feather and an anvil slide down the same frictionless ramp side by side. Galileo's result, arrived at from the algebra rather than the tower.

Add friction and the mass cancels a second time, which is the small miracle of this lesson. The toll is $f_k = \mu_k N = \mu_k\,mg\cos\theta$, and subtracting it from the drive gives $ma = mg\sin\theta - \mu_k\,mg\cos\theta$ — every term carries an $m$, so every term loses it: $a = g\left(\sin\theta - \mu_k\cos\theta\right)$, a equals g, bracket, sin theta minus mu-k cos theta. The sine term drives, the cosine term charges, and $\mu_k$ is the naked coefficient of kinetic friction.

Read the bracket and it tells you a story. If $\mu_k$ is large enough that $\mu_k\cos\theta$ reaches $\sin\theta$, the bracket hits zero: no acceleration, no slide. Rearrange that condition and you get $\mu = \tan\theta$ — the angle of repose, walking in from the last lesson through a completely different door. When two roads meet like that, the physics underneath is real.