A 640 N student stands on a bathroom scale in an elebator. As the elevator starts moving, the scale reads 800 N. a) find the acceleration of the elevator (magnitude and direction) b) acceleration if the scale reads 450N? c) If the scale reads 0 should the student worry? Explain.
a) was 2.45m/s^3 up
b) -2.91m/s^2
c) free fall, and worry but I don't understand why.
What were the equations used?
apparent weight = mass*g + mass*acceleration.
When it goes up, apparent weight is greater, when it goes down, apparent weight is smaller, in free fall, a= g, so
apparent wegith= mg-mg=0
In the free fall, what forces are acting on the scale and the student? Answer, exactly the same force (gravity) is accelerating both at the same rate, there is no apparent difference in acclerations (forces) between them.
To find the acceleration of the elevator in each scenario, the equation used is:
apparent weight = mass * g + mass * acceleration
where apparent weight is the reading on the scale, mass is the student's mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and acceleration is the acceleration of the elevator.
a) When the scale reads 800 N, we have:
800 N = (640 N) * 9.8 m/s^2 + (640 N) * acceleration
Rearranging the equation to solve for acceleration, we get:
acceleration = (800 N - (640 N) * 9.8 m/s^2) / (640 N)
Simplifying the calculation, we find that the acceleration is approximately 2.45 m/s^2 upward.
b) When the scale reads 450 N, we can use the same equation:
450 N = (640 N) * 9.8 m/s^2 + (640 N) * acceleration
Rearranging the equation to solve for acceleration, we get:
acceleration = (450 N - (640 N) * 9.8 m/s^2) / (640 N)
Simplifying the calculation, we find that the acceleration is approximately -2.91 m/s^2 downward. The negative sign indicates that the elevator is moving downward.
c) If the scale reads 0 N, it means that the apparent weight of the student is zero. This would only happen under the condition of free fall, where both the student and the scale are in a state of weightlessness (no apparent weight). In free fall, the acceleration of the elevator is equal to the acceleration due to gravity (approximately 9.8 m/s^2).
The reason the student should worry when the scale reads 0 N is because it indicates that the elevator is in a state of free fall, which means it is accelerating downward at the same rate as gravity. This can be a dangerous situation as the elevator is not being supported by any normal force, and if it were to hit the ground, it could lead to a crash or injury. Therefore, the student should be concerned and take necessary precautions.
Note: The explanation above assumes no air resistance and ideal conditions. In real-world scenarios, factors like air resistance may affect the exact values and outcomes.