A 44.0 kg man stands on a bathroom scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.90 m/s in 1.19 s. It travels with this constant speed in the upward direction for the next 7.60 s. The elevator then slows down (undergoes a uniform acceleration in the negative y direction) for 2.15 s and comes to rest. What does the bathroom scale register before the elevator starts to move? Answer in units of N. (Hint: What is the velocity of the elevator then?)
The elevator has not moved yet, so the normal force and the force of the man's weight are equal. The answer is 431.2 N
n - mg = ma
n - mg = 0, so
n = mg
n = 44.0*9.8
n = 431.2
To find out what the bathroom scale registers before the elevator starts to move, we need to consider the forces acting on the man when the elevator is at rest.
When the elevator is at rest, the man experiences two forces: his weight (mg) pulling him downwards, and the normal force (N) from the bathroom scale pushing him upwards.
Since the man is at rest, the net force acting on him must be zero. Therefore, we have the equation:
N - mg = 0
Solving for N, we find:
N = mg
where m is the mass of the man and g is the acceleration due to gravity, which is approximately 9.8 m/s².
Substituting the given mass of the man (44.0 kg) into the equation, we have:
N = 44.0 kg * 9.8 m/s²
Calculating this expression, we find:
N = 431.2 N
Therefore, the bathroom scale registers a reading of 431.2 N before the elevator starts to move.