The cable supporting a 2125 kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking. I would like step by step, with explanations behind the steps. Thank you :)
Well, well, well, seems like we have an elevator in a bit of a tight spot! Don't worry, I'm here to help you out, step by step, with a touch of humor to lighten the load!
First things first, let's analyze the situation. We know that the elevator has a mass of 2125 kg and the cable supporting it can withstand a maximum strength of 21,750 N. Now, we want to find the maximum upward acceleration without breaking that cable.
Step 1: Determine the force acting on the elevator
To do this, we use good old Newton's second law: F = m * a, where F is the force, m is the mass, and a is the acceleration. In this case, we are looking for the maximum acceleration, so let's plug in the values we have:
F = m * a
F = 2125 kg * a
Step 2: Set up the maximum force equation
Since the cable can withstand a maximum strength of 21,750 N, we can set up the following inequality:
F ≤ 21,750 N
Now, we can substitute the force equation from step 1 into this inequality:
m * a ≤ 21,750 N
Step 3: Solve for the maximum acceleration
To isolate the acceleration, we divide both sides of the inequality by the mass (m):
a ≤ 21,750 N / 2125 kg
Now, let's grab our calculators and do the math:
a ≤ 10.236 N/kg
So, the maximum upward acceleration the elevator can have without breaking the cable is approximately 10.236 m/s².
Remember, this is just the maximum acceleration the cable can withstand. It's always good to have a little buffer room in real-life situations, just like squeezing in some extra space for that overstuffed suitcase!
I hope my step-by-step explanation keeps you grounded while you elevate your understanding of the problem.
To determine the maximum upward acceleration the cable can provide without breaking, we need to consider the maximum tension in the cable. The tension in the cable is equal to the weight of the elevator plus the tension required to accelerate it.
Step 1: Calculate the weight of the elevator.
The weight of an object is calculated using the formula:
Weight = mass × acceleration due to gravity
Given:
Mass of the elevator (m) = 2125 kg
Acceleration due to gravity (g) = 9.8 m/s²
Using the formula, we can determine the weight of the elevator:
Weight = 2125 kg × 9.8 m/s² = 20,825 N
Step 2: Calculate the tension required to accelerate the elevator.
Since the elevator is moving upward, we need to consider the tension required to accelerate it against the force of gravity.
Tension = Weight + (mass × acceleration)
Given:
Weight = 20,825 N
Mass (m) = 2125 kg
Acceleration (a) = to be determined
Tension = 20,825 N + (2125 kg × a)
Step 3: Determine the maximum tension.
The maximum tension the cable can withstand is given as 21,750 N. Therefore, we can set up the equation:
Maximum tension = 21,750 N
Substituting the expression for tension we derived in Step 2:
21,750 N = 20,825 N + (2125 kg × a)
Step 4: Solve for acceleration (a).
Rearrange the equation to solve for acceleration:
(2125 kg × a) = 21,750 N - 20,825 N
(2125 kg × a) = 925 N
Divide both sides by 2125 kg to solve for a:
a = 925 N / 2125 kg
Step 5: Calculate the maximum upward acceleration.
Using a calculator, divide 925 N by 2125 kg to obtain the maximum upward acceleration:
a ≈ 0.435 m/s²
Therefore, the maximum upward acceleration the cable can provide without breaking is approximately 0.435 m/s².
To find the maximum upward acceleration the cable can provide without breaking, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
Here, F represents the force that the cable can exert without breaking, m is the mass of the elevator, and a is the maximum upward acceleration we are trying to find.
Given:
- Maximum force of the cable (F) = 21,750 N
- Mass of the elevator (m) = 2125 kg
Step 1: Substitute the given values into the formula.
21,750 N = 2125 kg * a
Step 2: Solve for a.
a = 21,750 N / 2125 kg
Now, divide the force by the mass to find the maximum upward acceleration.
Step 3: Calculate the maximum upward acceleration.
a = 10.235 N/kg
Therefore, the maximum upward acceleration the cable can provide without breaking is approximately 10.235 m/s².
f = m a
the net force is ... 21750 - m g = 21750 - 2125 * 9.81
divide net force by the mass to find max acceleration