A truck of mass 8000 kg is accelerating at 5.0 m/s2 up a hill of inclination 4 degrees to the horizontal. The friction forces on the truck add up to 550 N.

a) Draw a neat FBD of the truck indicating all the forces acting on it.
b) What force does the truck exert against the road in the direction of travel?
c) What force does the road exert on the truck in the direction of travel?
d) With the truck’s engine working just as hard, what would be the acceleration of the truck down the hill (again a FBD is needed)?

We cannot provide drawn figures

To answer these questions, we need to draw a free-body diagram (FBD) of the truck and identify all the forces acting on it. Let's go step by step.

a) FBD of the truck:
To draw the FBD, we represent the truck as a block and label the forces acting on it. Here are the forces involved:

1. Weight (mg): This force acts vertically downward and is equal to the mass of the truck (m) multiplied by the acceleration due to gravity (g = 9.8 m/s^2). In this case, the weight will be 8000 kg * 9.8 m/s^2.

---> mg
(downward)

2. Normal force (N): This force acts perpendicular to the inclined surface and supports the weight of the truck. Since the truck is on an incline, the normal force will not be equal to the weight. It can be calculated using the formula:

N = mg * cos(theta)

Here, theta (θ) is the angle of inclination, which is given as 4 degrees.

3. Friction force (f): The friction force acts opposite to the direction of motion. In this case, the friction forces on the truck add up to 550 N.

<--- f

4. Force exerted by the road in the direction of travel (F): This is the force we need to determine in question b and c.

Now let's move on to answering the questions.

b) Force exerted by the truck against the road in the direction of travel:
According to Newton's second law, the force exerted by the truck in the direction of travel can be calculated using the formula:

F = m * a

Here, m is the mass of the truck (8000 kg) and a is the acceleration (5.0 m/s^2). Plugging in these values will give you the answer.

c) Force exerted by the road on the truck in the direction of travel:
According to Newton's third law, the force exerted by the road on the truck in the direction of travel is equal in magnitude and opposite in direction to the force exerted by the truck (F) in question b.

d) Acceleration of the truck down the hill:
To determine the acceleration of the truck down the hill, we can use the same formula as in question b:

F = m * a

However, in this case, the force exerted by the truck against the road will be in the opposite direction than the force exerted by the road on the truck (because the truck is moving down the hill). Use the appropriate sign conventions to solve for the acceleration.

Finally, draw another FBD for the truck when it's moving down the hill to complete this answer.

I hope this explanation helps you understand how to approach and solve this problem.