Normal force on box on elevator floor?

In summary, the question asks for the magnitude of the normal force on a 12.0 kg box of sand on the floor of elevator cab A, which is connected by a cable to cab B. The tension in the cable is given as 1.86 x 10^4 N and the masses of the cabs are 1700 kg and 1200 kg respectively. The solution would involve considering the forces acting on the box and determining the conditions for it to remain motionless.
  • #1
GingerBread27
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0
In Fig. 5-42, elevator cabs A and B are connected by a short cable and can be pulled upward or lowered by the cable above cab A. Cab A has mass 1700 kg and cab B has mass 1200 kg. A 12.0 kg box of sand lies on the floor of cab A. The tension in the cable connecting the cabs is 1.86 x 10^4 N. What is the magnitude of the normal force on the box from the floor?

I don't even know where to start, please help?
 

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  • #2
Assuming the sand box isn't somehow connected to the bottom cable I think the question has a bunch of extraneous information. Consider what the conditions are to keep the box motionless. What forces are acting directly on the box?
 
  • #3


The normal force on the box can be calculated using the equation Fnet = ma, where Fnet is the net force acting on the box, m is the mass of the box, and a is the acceleration of the box. Since the box is at rest on the floor of cab A, the acceleration is 0 and the net force is also 0.

However, the box is also being pulled upward by the cable connecting the two cabs, which exerts a tension force of 1.86 x 10^4 N. This tension force is counteracted by the normal force from the floor, which must be equal in magnitude and opposite in direction to keep the box at rest.

Therefore, the magnitude of the normal force on the box is also 1.86 x 10^4 N. This means that the floor of cab A must be exerting a force of 1.86 x 10^4 N on the box to balance out the tension force and keep the box at rest.
 

1. What is the definition of "normal force"?

The normal force is the force that a surface exerts on an object that is in contact with it. It is perpendicular to the surface and acts in the opposite direction of the force applied by the object.

2. How does the normal force change in an elevator?

The normal force on a box in an elevator changes depending on the direction and speed of the elevator. When the elevator is stationary or moving at a constant speed, the normal force is equal to the weight of the box. However, when the elevator is accelerating or decelerating, the normal force will increase or decrease accordingly.

3. Why does the normal force change in an elevator?

The normal force changes in an elevator due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. When the elevator accelerates or decelerates, the box exerts a force on the elevator, and in turn, the elevator exerts an equal and opposite force on the box, resulting in a change in the normal force.

4. How does the weight of the box affect the normal force in an elevator?

The weight of the box affects the normal force in an elevator because the normal force is equal to the weight of the box when the elevator is stationary or moving at a constant speed. However, when the elevator is accelerating or decelerating, the normal force will be greater or less than the weight of the box.

5. Can the normal force on a box in an elevator ever be zero?

Yes, the normal force on a box in an elevator can be zero if the elevator is moving at a constant speed and there are no other forces acting on the box. This means that the weight of the box is equal to the force of gravity pulling it down, and there is no need for an additional normal force to keep the box in place.

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