Starting from rest, a 5.00 kg block slides 2.50 m down a rough 30.0 degree incline. The coefficient of kinetic friction between block and the incline is .436. Determine the work done by the friction force between block and incline and the work done on the normal force?

To determine the work done by the friction force and the work done on the normal force, we need to calculate the gravitational potential energy difference and the work done against friction.

1. Calculate the gravitational potential energy difference:
The change in height of the block when it slides down the incline is given by:
Δh = h2 - h1,
where h1 is the initial height and h2 is the final height.

Since the block starts from rest, it has no initial kinetic energy. Therefore, all the initial potential energy is converted into work.

The initial potential energy of the block is given by:
PE1 = m * g * h1,
where m is the mass of the block and g is the acceleration due to gravity.

The final potential energy of the block is given by:
PE2 = m * g * h2.

The gravitational potential energy difference is:
ΔPE = PE2 - PE1.

2. Determine the work done against friction:
The work done against friction is equal to the force of friction multiplied by the distance over which it acts.

The friction force is given by:
F_friction = μ * N,
where μ is the coefficient of kinetic friction and N is the normal force.

The normal force is given by:
N = m * g * cos(θ),
where θ is the angle of the incline.

The total work done against friction is:
W_friction = F_friction * d,
where d is the distance the block slides down the incline.

Once we have calculated these values, we can determine the work done by the friction force and the work done on the normal force.

Note: In this explanation, g is taken as the magnitude of acceleration due to gravity (9.8 m/s^2), unless specified otherwise in the problem.

Hope this helps! Let me know if you have any further questions.