Computer Box Sliding in an Elevator: Magnitude of Applied Force Calculation
What magnitude of force must be applied to slide a computer box at a constant speed in an elevator accelerating upwards?
Given data: elevator's upward acceleration = 1.94 m/s², total mass of the box and contents = 28.4 kg, coefficient of kinetic friction (μk) = 0.35.
Answer:
117 N
Explanation:
You want the horizontal force applied to a 28.4 kg box to sustain horizontal motion when it is being accelerated upward in an elevator at 1.94 m/s², and its μk = 0.35.
Normal force:
The normal force at the box-floor interface is the sum of its weight due to gravity and the force required to accelerate it upward. That force is Fn = ma = (28.4 kg)(1.94 m/s² + 9.81 m/s²) = 333.7 N.
Horizontal force:
The force necessary to sustain motion is that required to counter the friction force: Fh = μk·Fn = 0.35·333.7 N = 116.795 N ≈ 117 N.
About 117 newtons must be applied to slide the box.
To slide a box at constant speed in an accelerating elevator, you must apply a horizontal force equal in magnitude to the force of kinetic friction. This force can be found using the mass of the box, the elevator's acceleration, gravity, and the coefficient of kinetic friction.
To find the magnitude of force you must apply to slide the box at a constant speed while the elevator is accelerating upward, we need to consider two forces: the force of kinetic friction and the horizontal force you apply. The kinetic friction force is determined by multiplying the normal force (which is equal to the gravitational force plus the force due to the elevator's acceleration) by the coefficient of kinetic friction (μm).
The normal force (N) is calculated by considering the forces in the vertical direction: N = mg + ma, where m is the mass of the box, g is the acceleration due to gravity (9.81 m/s²), and a is the acceleration of the elevator. Once we have the normal force, we can calculate the frictional force: F_friction = μm * N.
Since the box slides at a constant speed, the net force in the horizontal direction must be zero, which means the force you apply (F_apply) must be equal in magnitude to the frictional force. Therefore, F_apply = F_friction.
Example Calculation:
First, calculate the normal force: N = mg + ma = (28.4 kg)(9.81 m/s²) + (28.4 kg)(1.94 m/s²) = 333.516 N.
Now, calculate the force of friction: F_friction = μm * N = 0.35 * 333.516 N = 116.7306 N.
Finally, the magnitude of the force you must apply: F_apply = 116.7306 N.