Answer: When a person stands on a bathroom scale, the reading on the scale (called the apparent weight) is equal to the normal force acting on the person. Let's analyze the strength of the normal force relative to the force of gravity in different scenarios:
Explanation: a) When the elevator is stationary:
In this case, the elevator is not moving, so its acceleration is zero. Therefore, the normal force is equal to the force of gravity acting on the person. Since the person's mass is 75 kg, the force of gravity can be calculated using the formula F = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s²). So, the normal force would be (75 kg) * (9.8 m/s²).
b) When the elevator accelerates upwards at 0.25 m/s²:
In this scenario, the elevator is accelerating upwards. The normal force will be greater than the force of gravity. To calculate the normal force, we need to consider the net force acting on the person. The net force is given by the equation F_net = m * a, where m is the mass of the person and a is the acceleration of the elevator. Therefore, the normal force would be the sum of the force of gravity and the net force: (75 kg) * (9.8 m/s²) + (75 kg) * (0.25 m/s²).
c) When the elevator accelerates downwards at 0.6 m/s²:
In this case, the elevator is accelerating downwards. The normal force will be less than the force of gravity. Similar to the previous scenario, the normal force is the sum of the force of gravity and the net force. However, since the acceleration is in the opposite direction, we subtract the net force from the force of gravity: (75 kg) * (9.8 m/s²) - (75 kg) * (0.6 m/s²).
d) When the elevator is moving upwards at a constant velocity:
When the elevator is moving upwards at a constant velocity, there is no acceleration. Therefore, the normal force is equal to the force of gravity, similar to the stationary scenario: (75 kg) * (9.8 m/s²).
By following these steps, you can determine the strength of the normal force relative to the force of gravity in different elevator scenarios.