a blockof mass 100 kg tied to a donkey that moves with constant accelaration of 20centimeter over second squared up a 30 degrees incline. what is the force with which the donkey pulls on the block parallel to the incline? The coefficient of kinetic friction between the kinetic friction between the incline and the box is 0.30.

To find the force with which the donkey pulls the block parallel to the incline, we need to consider the various forces acting on the block.

The forces acting on the block include:
1. Weight (mg): The force due to gravity, which is equal to the mass (m) of the block multiplied by the acceleration due to gravity (g). In this case, the weight acts vertically downward and can be calculated as: Weight = mass (m) * acceleration due to gravity (g).

2. Normal force (N): The force exerted by the incline surface perpendicular to the incline. It acts in a direction perpendicular to the incline and balances the component of the weight that is perpendicular to the incline. The normal force can be calculated as: Normal force = Weight * cos(angle of incline).

3. Kinetic friction force (fk): The force opposing the motion of the block along the incline. It acts parallel to the incline and can be calculated as: Kinetic friction force = coefficient of kinetic friction (μk) * Normal force.

4. Force of donkey pulling parallel to the incline: Let's denote this force as F.

Considering that the block is moving up the incline with a constant acceleration, we can apply Newton's second law in the direction parallel to the incline:

Sum of forces parallel to the incline (F - fk) = mass of the block (m) * acceleration.

As we are looking for the force with which the donkey pulls the block parallel to the incline, we can rearrange the equation as:

F = mass of the block (m) * acceleration + fk.

Now, we can substitute the given values into the equation to calculate the force (F):
- mass of the block (m) = 100 kg.
- acceleration = 20 cm/s^2 = 0.2 m/s^2 (since 1 meter = 100 centimeters).
- angle of incline = 30 degrees.
- coefficient of kinetic friction (μk) = 0.30.

First, we need to calculate the weight of the block:
Weight = mass (m) * acceleration due to gravity (g).
Weight = 100 kg * 9.8 m/s^2 (approximating the acceleration due to gravity).
Weight = 980 N.

Next, we can calculate the normal force:
Normal force = Weight * cos(angle of incline).
Normal force = 980 N * cos(30 degrees).
Normal force = 980 N * 0.866 (approximating the cosine of 30 degrees).
Normal force ≈ 848.7 N.

Then, we can calculate the kinetic friction force:
Kinetic friction force = coefficient of kinetic friction (μk) * Normal force.
Kinetic friction force = 0.30 * 848.7 N.
Kinetic friction force ≈ 254.6 N.

Finally, we can calculate the force with which the donkey pulls the block parallel to the incline:
F = mass of the block (m) * acceleration + fk.
F = 100 kg * 0.2 m/s^2 + 254.6 N.
F ≈ 20 N + 254.6 N.
F ≈ 274.6 N.

Therefore, the force with which the donkey pulls on the block parallel to the incline is approximately 274.6 Newtons.