A child accelerates upwards in an elevator which causes his apparent weight to become 405N. Determine the magnitude of the elevators acceleration if his normal weight is 400N.
m g = 400
m = 400/g
m g + m a = 405
(400/g)(g+a) = 405
400 (g+a) = 405 g
400 a = 5 g
a = g/80 = .123 m/s^2
To determine the magnitude of the elevator's acceleration, we need to start by understanding the forces acting on the child in the elevator.
The apparent weight of the child can be thought of as the force exerted on the child due to his own weight and the force exerted on the child by the elevator. The normal weight of the child is 400N, so this is the force due to his own weight.
The force exerted on the child by the elevator is the net force acting on him. In this case, the net force is directed upwards and has a magnitude of 405N.
Now, let's denote the acceleration of the elevator as "a" and the mass of the child as "m". According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the net force acting on the child is the difference between the force due to his own weight and the force exerted on him by the elevator:
Net force = force due to weight - force exerted by elevator.
Net force = m * a - m * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Since the child is accelerating upwards, the acceleration due to gravity needs to be subtracted. Thus, the equation becomes:
Net force = m * (a - g)
We are given that the net force acting on the child is 405N, and his normal weight (force due to his own weight) is 400N. So we have:
405N = m * (a - 9.8 m/s²)
Now, we can solve for the acceleration, "a":
a - 9.8 m/s² = 405N / m
a = (405N / m) + 9.8 m/s²
To find the magnitude of the elevator's acceleration, we need to know the mass of the child. Without that information, we cannot determine the magnitude of the elevator's acceleration.