Determine the normal force for a laundry basket with a mass of 4.3 kg in each of the following situations

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To determine the normal force acting on the laundry basket in different situations, we need to consider the forces involved. The normal force is the force exerted by a surface to support the weight of an object resting on it.

Situation 1: When the basket is placed on a horizontal surface without any other forces acting on it.

In this situation, the normal force is equal to the weight of the basket since the weight is balanced by the normal force.

The weight of the basket can be calculated using the formula:
weight = mass × gravitational acceleration

Given that the mass of the basket is 4.3 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight:

weight = 4.3 kg × 9.8 m/s^2 = 42.14 N

Therefore, in this situation, the normal force acting on the basket is 42.14 N.

Situation 2: When the basket is placed on an inclined plane.

In this situation, the normal force can be calculated using trigonometry. The normal force is perpendicular to the surface and is equal in magnitude and opposite in direction to the component of the weight that is perpendicular to the surface.

The weight can be split into two components: one parallel to the surface (mg•sinθ) and the other perpendicular to the surface (mg•cosθ), where θ is the angle of inclination.

Since the basket is on an inclined plane, the perpendicular component (mg•cosθ) of the weight is equal to the normal force.

Given the mass of the basket as 4.3 kg and the angle of inclination θ, you can determine the normal force using the formula:
normal force = weight perpendicular = mass × gravitational acceleration × cosθ

Calculate the normal force using the given values for mass, gravitational acceleration, and angle of inclination.

Once you have the angle of inclination, plug in the values and solve the equation to find the normal force.

Remember to convert the angle to radians if necessary.

Situation 3: When the basket is in free fall.

In this situation, the normal force is zero because there is no surface to exert a force on the basket. The weight of the basket would be balanced by the force of gravity pulling it downward.

Please note that in free fall, the question of normal force does not arise as there is no surface to provide the force.

To summarize:
1. In a horizontal situation, the normal force equals the weight of the basket.
2. On an inclined plane, the normal force equals the perpendicular component of the weight, which can be calculated using the formula provided.
3. In free fall, where there is no surface, the normal force is zero.