A 12.0kg bucket is lowered vertically by a rope in which there is 180 N of tension at a given instant.
What is the acceleration of the bucket?
Is it up or down?
If you draw a free-body diagram for the bucket, you will end up with the following (shown sideways)
TOP---->180N<------BUCKET-------->12g N BOTTOM
Since 180N > 12g=12*9.8=117.6
the acceleration is upwards.
Net upward force = 180-117.6,
mass = 12 kg
Acceleration = ??? using F=ma
To find the acceleration of the bucket, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration, or F = ma.
In this case, the net force acting on the bucket is the tension in the rope. The tension is given as 180 N.
So, we have F = 180 N and the mass of the bucket is 12.0 kg.
Using Newton's second law, we can rearrange the equation to solve for acceleration:
F = ma
180 N = 12.0 kg * a
Dividing both sides of the equation by 12.0 kg, we get:
a = 180 N / 12.0 kg
Simplifying, we find:
a = 15.0 m/s^2
Therefore, the acceleration of the bucket is 15.0 m/s^2.
To determine whether the bucket is moving up or down, we need to consider the direction of the net force. In this case, the tension in the rope is acting in the upward direction. Since the force is acting in the opposite direction of the acceleration, the bucket will be moving downward.
Therefore, the bucket is accelerating downward with an acceleration of 15.0 m/s^2.
To determine the acceleration of the bucket, we first need to understand the forces acting on it. In this scenario, we know that the tension in the rope is 180 N. Additionally, there is the force of gravity acting on the bucket, which can be calculated using the equation:
Weight (W) = mass (m) * acceleration due to gravity (g)
Given that the mass of the bucket is 12.0 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the bucket:
W = 12.0 kg * 9.8 m/s^2
W = 117.6 N
Since the tension in the rope is greater than the weight of the bucket (180 N > 117.6 N), the net force acting on the bucket is upwards. This is why the rope is able to support the bucket and prevent it from falling.
Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force (F_net) = mass (m) * acceleration (a)
In this case, we can rewrite this equation as:
Tension - Weight = mass * acceleration
180 N - 117.6 N = 12.0 kg * acceleration
Simplifying this equation, we get:
62.4 N = 12.0 kg * acceleration
To find the acceleration, we can rearrange the equation:
acceleration = 62.4 N / 12.0 kg
acceleration ≈ 5.2 m/s^2
So, the acceleration of the bucket is approximately 5.2 m/s^2.
Additionally, since the net force is upwards (as tension is greater than weight), the bucket accelerates in the upward direction.