To solve this problem, we will use principles of energy conservation and work-energy theorem.

Step 1: Work without friction

First, let's calculate the energy and speed of the block when there is no friction (already provided):

• Mass of the block $m = 8.90 \, \text{kg}$
• Length of the ramp $d = 1.32 \, \text{m}$
• Initial speed $v_i = 0 \, \text{m/s}$
• Final speed without friction $v_f = 2.99 \, \text{m/s}$

The mechanical energy is conserved. The initial potential energy (PE) of the block is completely converted into kinetic energy (KE) at the bottom:

$PE = KE$

$mgh = \frac{1}{2}mv_f^2$

where $h$ is the vertical height of the ramp.

We can find the height using the length of the ramp and the fact that the ramp is inclined:

$h = \frac{v_f^2}{2g}$

Step 2: With Friction

Now, when friction is acting, the work-energy theorem states:

$KE_{final} = PE_{initial} - W_{friction}$ where:

• $W_{friction} = f \cdot d$, and $f = 10.1 \, \text{N}$,