The cable supporting a 2100kg elevator has a maximum strength of 2.19×10^4 N.
What maximum upward acceleration can it give the elevator without breaking?
mass = 2100 kg
weight
= mg
= 2100 kg *9.8 m/s/s
=20580 N
Strength
=21900 N
Reserve capacity for upwards acceleration, F
=21900-20580
=1320N
Use F=ma to find a. It will be less than 1 m/s/s.
I just hope this is not a real life problem.
To find the maximum upward acceleration that the cable can give to the elevator without breaking, we need to use Newton's second law of motion, which states that the force exerted on an object is equal to the product of its mass and acceleration.
The force exerted on the elevator is its weight, given by the formula:
Force = mass x acceleration due to gravity
Given that the mass of the elevator is 2100 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force as:
Force = 2100 kg x 9.8 m/s^2 = 20580 N
We are given that the maximum strength of the cable is 2.19×10^4 N. In order for the cable not to break, the force exerted on the elevator must be less than or equal to the maximum strength of the cable. Therefore, we can set up the following inequality:
20580 N ≤ 2.19×10^4 N
Now, we can solve this inequality to find the maximum upward acceleration:
20580 N ≤ 2.19×10^4 N
Divide both sides by 20580 N:
1 ≤ (2.19×10^4 N) / 20580 N
1 ≤ 1.0622
Since 1 is less than or equal to 1.0622, the maximum upward acceleration that the cable can give the elevator without breaking is less than or equal to 1.0622 m/s^2.
To determine the maximum upward acceleration that the cable can provide without breaking, we need to consider the tension in the cable.
The tension in the cable can be calculated using the formula:
Tension = mass * acceleration
Given:
Mass of the elevator (m) = 2100 kg
Maximum strength of the cable (maximum tension, T) = 2.19 × 10^4 N
Let's rearrange the formula to solve for acceleration:
acceleration = Tension / mass
Substituting the given values into the equation:
acceleration = (2.19 × 10^4 N) / (2100 kg)
Simplifying the equation:
acceleration = 2.19 × 10^4 / 2100
Now, let's calculate the value:
acceleration = 10.43 m/s²
Therefore, the maximum upward acceleration the cable can provide without breaking is 10.43 m/s².