The tension in a string from which a 6 kg
object is suspended in an elevator is equal to 61 N.
What is magnitude of the acceleration a of the elevator? The acceleration of gravity is
9.8 m/s^2.
Answer in units of m/s^2
61 N up
6*9.8 = 58.8 down
net force on object = 2.2 N up
F = m a
2.2 = 6 a
a = 2.2/6 = .367 m/s^2
Well, if you're looking for some lift, I can definitely provide you with an answer! Let's untangle this problem together.
The tension in the string is equal to the force gravity exerts on the object, which can be calculated as the product of its mass (6 kg) and the acceleration due to gravity (9.8 m/s^2). So the force of gravity is 6 kg × 9.8 m/s^2 = 58.8 N.
However, since the tension in the string is given as 61 N, we know there's an additional force at play. This force is the so-called pseudo-force or apparent weight caused by the acceleration of the elevator.
To find the acceleration of the elevator, we need to calculate the net force acting on the object. This can be found by subtracting the force of gravity from the tension: 61 N - 58.8 N = 2.2 N.
Now, knowing that force equals mass times acceleration, we can rearrange the equation to solve for acceleration: acceleration = force / mass = 2.2 N / 6 kg = 0.367 m/s^2.
So, the magnitude of the acceleration of the elevator is approximately 0.367 m/s^2. That's not too shabby for an elevator trying to lift 6 kg... it's really crushing it!
To find the magnitude of the acceleration of the elevator, we need to consider the forces acting on the object. In this case, we have the tension in the string and the force due to gravity.
The force due to gravity can be calculated using the equation:
Force due to gravity = mass * acceleration due to gravity
Given:
Mass = 6 kg
Acceleration due to gravity = 9.8 m/s^2
Force due to gravity = 6 kg * 9.8 m/s^2 = 58.8 N
Since the tension in the string is equal to 61 N, and the force due to gravity is 58.8 N, the net force on the object is the difference between these two forces:
Net force = Tension - Force due to gravity
Net force = 61 N - 58.8 N = 2.2 N
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = mass * acceleration
2.2 N = 6 kg * acceleration
Solving for acceleration gives:
acceleration = 2.2 N / 6 kg = 0.367 m/s^2
Therefore, the magnitude of the acceleration of the elevator is 0.367 m/s^2.
To find the magnitude of the acceleration of the elevator, we can use Newton's second law of motion. The tension in the string is equal to the force acting on the object, which is given as 61 N.
According to Newton's second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the mass of the object is given as 6 kg.
So, we have the equation:
Tension = mass * acceleration
61 N = 6 kg * acceleration
Now, we can solve for the acceleration by rearranging the equation:
acceleration = tension / mass
acceleration = 61 N / 6 kg
Plugging in the given values, we have:
acceleration = 10.17 m/s^2
Therefore, the magnitude of the acceleration of the elevator is 10.17 m/s^2.