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
ma=-mg+N
N=ma+mg
To find the upward force exerted by the floor of the elevator on the passenger, we need to calculate the net force acting on the passenger.
The net force can be calculated using Newton's second law of motion, which states that the net force equals the mass of an object multiplied by its acceleration:
Net force = mass × acceleration
Given:
Mass of the passenger (m) = 92 kg
Acceleration of the elevator (a) = 1.2 m/s^2
Acceleration due to gravity (g) = 9.8 m/s^2
To calculate the net force, we first need to determine the weight of the passenger, which is the force due to gravity acting on the passenger's mass:
Weight = mass × acceleration due to gravity
Weight = 92 kg × 9.8 m/s^2
Weight = 901.6 N
Since the elevator is accelerating upward, the net force acting on the passenger can be represented as:
Net force = Upward force - Weight
Considering that the floor of the elevator is exerting an upward force on the passenger, we can rearrange the equation to solve for the upward force:
Upward force = Net force + Weight
Upward force = mass × acceleration + Weight
Upward force = 92 kg × 1.2 m/s^2 + 901.6 N
Upward force = 110.4 N + 901.6 N
Upward force = 1012 N
Therefore, the upward force exerted by the floor of the elevator on the 92 kg passenger is 1012 N.
To find the upward force exerted by the floor of the elevator on the passenger, we need to use Newton's second law of motion, which states that force (F) is equal to the mass (m) multiplied by the acceleration (a).
Here's how we can calculate it step by step:
1. Calculate the weight of the passenger. The weight is given by the formula W = mg, where m is the mass of the passenger (92 kg) and g is the acceleration due to gravity (9.8 m/s^2).
W = 92 kg × 9.8 m/s^2
W = 901.6 N
2. Considering the upward acceleration of the elevator, we need to take into account the net force acting on the passenger. The net force can be calculated using the formula F = ma, where m is still the mass of the passenger (92 kg) and a is the acceleration of the elevator (1.2 m/s^2).
F = 92 kg × 1.2 m/s^2
F = 110.4 N
Since the elevator is accelerating upwards, the upward force exerted by the floor of the elevator on the passenger must be greater than the downward force caused by the passenger's weight. Therefore, we need to add the weight and the net force:
Total upward force = Weight + Net force
Total upward force = 901.6 N + 110.4 N
Total upward force = 1012 N
So, the upward force exerted by the floor of the elevator on the 92 kg passenger is 1012 N.