Rachel pulls her 177N suitcase at a constant speed by pulling on a handle that makes an angle (-) with the horizontal. Using frictional force on the suitcase as 27N and Rachels force on 43N on the handle to calculate the net force.

1. What angle does the handle make with the horizontal (since velocity is constant, the frictional force and horizontal component of the applied force are equal.

2. What is the Normal force exerted on the suitcase?

1. To find the angle that the handle makes with the horizontal, we can use the fact that the frictional force and horizontal component of the applied force are equal. Since the suitcase is being pulled at a constant speed, the net force in the horizontal direction must be zero.

The horizontal component of Rachel's force can be found using the cosine of the angle between the applied force (F_app) and the horizontal direction:

Horizontal component of F_app = F_app * cos(angle)

Given that the applied force is 43N, we can solve for the angle as follows:

Horizontal component of F_app = 27N (due to frictional force)
43N * cos(angle) = 27N

Solving for angle:
cos(angle) = 27N / 43N
cos(angle) = 0.628
angle = arccos(0.628)
angle ≈ 50.03 degrees

Therefore, the angle that the handle makes with the horizontal is approximately 50.03 degrees.

2. The normal force exerted on the suitcase can be found using Newton's second law, which states that the sum of forces in the vertical direction is equal to the mass of the object times its vertical acceleration (which is zero in this case).

The normal force is the force exerted by a surface, perpendicular to that surface. In this case, it is the force exerted by the ground on the suitcase, counteracting the force of gravity.

Considering the equilibrium in the vertical direction, we have:

Net force in the vertical direction = 0

Vertical component of F_app - Weight of the suitcase = 0

The weight of the suitcase is given by:

Weight = mass * gravitational acceleration

We do not have the mass of the suitcase, but we can solve for the normal force in terms of the weight:

Vertical component of F_app = Weight

Vertical component of F_app = mass * gravitational acceleration

Vertical component of F_app = Weight = mg

The normal force (equal in magnitude but opposite in direction to the weight) can therefore be given as:

Normal force = -mg

Since the weight acts downwards, the normal force acts upwards. We can only determine the magnitude of the normal force, not the direction.

Therefore, in this case, the normal force exerted on the suitcase is equal to its weight, which is mg, where m is the mass of the suitcase and g is the acceleration due to gravity.