The tension in a string from which a 4.0 kg object is suspended in an elevator is equal to 44 N. What is the acceleration of the elevator?
Understand the Problem
The question is asking us to find the acceleration of an elevator given the tension in the string and the weight of the suspended object. We will use the concepts of forces and Newton's second law to solve for the acceleration.
Answer
$$ a = \frac{T - mg}{m} $$
Answer for screen readers
The acceleration of the elevator is given by:
$$ a = \frac{T - mg}{m} $$
Steps to Solve
- Identify the forces acting on the suspended object
In this scenario, we have two main forces acting on the suspended object: the tension in the string ($T$) and the weight of the object ($W$). The weight can be calculated using the formula:
$$ W = mg $$
where $m$ is the mass of the object and $g$ is the acceleration due to gravity (approximately $9.81 , \text{m/s}^2$).
- Write down Newton's second law equation
Next, we can apply Newton's second law. The net force ($F_{net}$) acting on the object will be the difference between the tension and the weight:
$$ F_{net} = T - W $$
According to Newton's second law, we can express the net force in terms of mass and acceleration ($a$):
$$ F_{net} = ma $$
- Set the equations equal and solve for acceleration
We can now set the two expressions for net force equal to each other:
$$ T - mg = ma $$
Now, we can isolate $a$:
$$ a = \frac{T - mg}{m} $$
- Substitute known values
Finally, substitute the known values for tension ($T$), mass ($m$), and gravitational acceleration ($g$) into the equation we derived:
$$ a = \frac{T - mg}{m} $$
The acceleration of the elevator is given by:
$$ a = \frac{T - mg}{m} $$
More Information
The acceleration you find will indicate how quickly the elevator is speeding up or slowing down. A positive acceleration means the elevator is going up, while a negative acceleration indicates it is descending.
Tips
- Forgetting to convert mass from grams to kilograms if not already done.
- Neglecting the direction of forces; always remember tension acts upwards while weight acts downwards.
- Not including the correct value of gravitational acceleration; always use $9.81 , \text{m/s}^2$ unless otherwise specified.
AI-generated content may contain errors. Please verify critical information
