Your engineering firm is asked to specify the maximum load for the elevators in a new building. Each elevator has mass 500 kg when empty and maximum acceleration 2.25 m/s^2. The elevator cables can withstand a maximum tension of 19.6 kN before breaking. For safety, you need to ensure that the tension never exceeds two-thirds of that value. What do you specify for the maximum load?How many 75.0-\rm kg people is that?
Maximum elevator load = M*g, where M is the mass of passengers and/or freight.
Require that
(500 + M)*(g + a) = 1.5 * Tmax
(500 + M)*12.05 = 29.4*10^3 N
Solve for M.
M = 2440 kg
Divide M by 75 kg for the maximum number of people.
a.)588.88 kg
b.) 7
To specify the maximum load for the elevators, we need to consider the maximum tension the elevator cables can withstand and the maximum acceleration of the elevators.
Given:
Mass of each elevator (empty) = 500 kg
Maximum acceleration of elevators = 2.25 m/s^2
Maximum tension elevator cables can withstand = 19.6 kN
Safety factor for tension = 2/3
Step 1: Maximum tension the elevator cables can withstand with the safety factor
Maximum tension = (2/3) * Maximum tension elevator cables can withstand
Maximum tension = (2/3) * 19.6 kN = 13.07 kN
Step 2: Calculate the maximum load
Using Newton's second law of motion: Force = mass * acceleration
Maximum tension = Maximum load * acceleration
13.07 kN = Maximum load * 2.25 m/s^2
Maximum load = 5.80 kN
Step 3: Convert the maximum load to number of 75.0 kg people
To do this, we need to find the total mass that the elevator can carry.
Using Newton's second law of motion: Force = mass * acceleration
Maximum load = Total mass * acceleration
5.80 kN = Total mass * 2.25 m/s^2
Total mass = 2.58 kN
Now, to find the number of 75.0 kg people:
Number of 75.0 kg people = Total mass / mass of each person
Number of 75.0 kg people = 2.58 kN / 75.0 kg = 34.4 people
Therefore, the specified maximum load for the elevators is 5.80 kN, which is equivalent to carrying approximately 34.4 75.0 kg people.
To determine the maximum load that the elevators can carry, you need to consider the maximum tension that the elevator cables can withstand. In this case, the maximum tension before breaking is given as 19.6 kN, and for safety, you must ensure that the tension never exceeds two-thirds of that value.
The maximum tension allowed is two-thirds of 19.6 kN, which can be calculated as: (2/3) * 19.6 kN = 2/3 * 19.6 * 1000 N (since 1 kN = 1000 N) = 2/3 * 19.6 * 1000 N = 13.07 * 1000 N = 13,070 N.
The tension in the elevator cables is directly related to the weight of the elevator when it is loaded. Using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration, we can find the maximum load.
The force acting on the elevator is equal to the tension in the elevator cables. Let's assume the maximum load is 'm' kg. Then, the force acting on the elevator due to its mass and acceleration can be calculated as follows:
Force = Mass * Acceleration
13,070 N = (m kg + 500 kg) * 2.25 m/s^2
Now, let's solve this equation to find the value of 'm' which represents the maximum load the elevator can carry.
13,070 N = (m + 500 kg) * 2.25 m/s^2
Dividing both sides by 2.25 m/s^2,
m + 500 kg = 5804 kg
Subtracting 500 kg from both sides,
m = 5304 kg
Therefore, you can specify the maximum load as 5304 kg for each elevator in the building.
To determine the number of 75.0 kg people that the elevator can hold, divide the maximum load by the weight of each person:
Number of people = Maximum load / Weight per person
Number of people = 5304 kg / 75.0 kg
Number of people ≈ 70.72
Since you cannot have a fraction of a person, the elevator can hold a maximum of 70 people with a weight of 75.0 kg each.