Normal Force and Tension on suitcase strap

In summary, the problem involves pulling a 21.9-kg suitcase with a strap at a 46.1° angle above the horizontal at the airport. The task is to calculate the normal force in the strap, assuming the suitcase moves at a constant speed and the coefficient of kinetic friction between the suitcase and the floor is 0.380. Additionally, the tension in the strap must also be calculated.
  • #1
purcell2
2
0
At the airport, you pull a 21.9-kg suitcase across the floor with a strap that is at an angle of 46.1° above the horizontal. Calculate the normal force in the strap, given that the suitcase moves with constant speed and that the coefficient of kinetic friction between the suitcase and the floor is 0.380. Calculate the Tension in the strap.
 
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  • #2
purcell2 said:
At the airport, you pull a 21.9-kg suitcase across the floor with a strap that is at an angle of 46.1° above the horizontal. Calculate the normal force in the strap, given that the suitcase moves with constant speed and that the coefficient of kinetic friction between the suitcase and the floor is 0.380. Calculate the Tension in the strap.

What is your approach to the problem?
 
  • #3


I would first like to clarify the definitions of normal force and tension in this scenario. The normal force is the force exerted by the surface on the object in a direction perpendicular to the surface. In this case, it would be the force exerted by the floor on the suitcase. On the other hand, tension is the force exerted on an object by a string, rope, or any other type of flexible material.

Using the given information, we can calculate the normal force on the strap by first finding the weight of the suitcase. We know that weight is equal to mass times acceleration due to gravity (w=mg). Therefore, the weight of the suitcase would be (21.9 kg)(9.8 m/s^2) = 214.62 N. Since the suitcase is moving with constant speed, we can assume that the net force on the suitcase is zero. This means that the normal force must be equal in magnitude and opposite in direction to the weight of the suitcase. Therefore, the normal force on the strap would also be 214.62 N.

To calculate the tension in the strap, we can use the equation T = μkN, where μk is the coefficient of kinetic friction and N is the normal force. Plugging in the values, we get T = (0.380)(214.62 N) = 81.6 N. This means that the tension in the strap is 81.6 N.

In conclusion, the normal force on the strap is 214.62 N and the tension in the strap is 81.6 N. These values are important to consider when designing and using straps for luggage or other objects. By understanding the forces at play, we can ensure that the strap is strong enough to withstand the tension and that the surface it is being pulled on can provide enough normal force to keep the object moving at a constant speed.
 

1. What is the difference between normal force and tension on a suitcase strap?

The normal force on a suitcase strap is the force exerted by the strap on the suitcase in a direction perpendicular to the surface of the suitcase. This force is responsible for keeping the suitcase from falling through the strap. Tension, on the other hand, is the force exerted by the strap on the suitcase in a direction parallel to the surface of the suitcase. This force is responsible for keeping the strap taut and preventing the suitcase from moving away from the strap.

2. How does the weight of the suitcase affect the normal force and tension on the strap?

The weight of the suitcase directly affects the normal force and tension on the strap. As the weight of the suitcase increases, the normal force and tension on the strap also increase. This is because the weight of the suitcase exerts a downward force on the strap, causing the strap to exert an equal and opposite force, resulting in an increase in both the normal force and tension.

3. Can the normal force and tension on a suitcase strap ever be equal?

Yes, the normal force and tension on a suitcase strap can be equal if the suitcase is at rest and not moving. In this case, the normal force exerted by the strap is equal to the weight of the suitcase, and the tension in the strap is also equal to the weight of the suitcase. This is an example of a balanced force system, where all forces acting on the suitcase are equal and opposite, resulting in no net force and therefore no acceleration.

4. How does the angle of the strap affect the normal force and tension on a suitcase?

The angle of the strap affects both the normal force and tension on a suitcase. As the angle of the strap increases, the tension in the strap also increases, while the normal force decreases. This is because a larger angle results in a greater component of the weight of the suitcase being supported by the tension in the strap, while a smaller component is supported by the normal force.

5. Can the normal force and tension on a suitcase strap be negative?

No, the normal force and tension on a suitcase strap cannot be negative. Negative forces indicate a direction opposite to the chosen coordinate system and do not have a physical meaning in this scenario. Both the normal force and tension on a suitcase strap will always be positive or zero, depending on the weight of the suitcase and the angle of the strap.

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