007 (part 1 of 2)
An elevator accelerates upward at 1.2 m/s2. The acceleration of gravity is 9.8 m/s2 . What is the upward force exerted by the
floor of the elevator on a(n) 92 kg passenger? Answer in units of N
008 (part 2 of 2)
If the same elevator accelerates downwards with an acceleration of 1.2 m/s2, what is the upward force exerted by the elevator floor on the passenger?
Answer in units of N
Just reverse the sign of the acceleration from your last question.
To solve these problems, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
For 007 (part 1 of 2):
1. Calculate the force of gravity acting on the passenger using the formula Fg = m * g, where m is the mass (92 kg) and g is the acceleration due to gravity (9.8 m/s^2).
Fg = 92 kg * 9.8 m/s^2 = 901.6 N
2. Calculate the force exerted by the floor of the elevator using the formula F = m * a, where m is the mass (92 kg) and a is the acceleration of the elevator (1.2 m/s^2).
F = 92 kg * 1.2 m/s^2 = 110.4 N
3. Since the elevator is accelerating upwards, the net force acting on the passenger is the sum of the force of gravity and the force exerted by the floor.
Net force = Fg + F = 901.6 N + 110.4 N = 1012 N
Therefore, the upward force exerted by the floor of the elevator on the 92 kg passenger is 1012 N.
For 008 (part 2 of 2):
The process is similar to the previous question, but this time the elevator is accelerating downwards.
1. The force of gravity acting on the passenger remains the same: Fg = m * g = 92 kg * 9.8 m/s^2 = 901.6 N.
2. Calculate the force exerted by the floor of the elevator, which is now in the opposite direction of the acceleration (upwards):
F = m * a = 92 kg * (-1.2 m/s^2) = -110.4 N
Note that the negative sign indicates the opposite direction of the force due to the acceleration downwards.
3. The net force acting on the passenger is the sum of the force of gravity and the force exerted by the floor:
Net force = Fg + F = 901.6 N - 110.4 N = 791.2 N
Therefore, the upward force exerted by the floor of the elevator on the 92 kg passenger, when it is accelerating downwards with an acceleration of 1.2 m/s^2, is 791.2 N.