A 14.0 kg bucket is lowered vertically by a rope in which there is 181 N of tension at a given instant.
What is the acceleration of the bucket?
May someone please walk me through this problem step by step. Thank you
ma=mg-T
a=g- (T/m)
Sure! Let's walk through this step by step.
Step 1: Understand the problem
In this problem, we have a bucket being lowered vertically by a rope. We are given the mass of the bucket (14.0 kg) and the tension in the rope (181 N). We need to find the acceleration of the bucket.
Step 2: Identify the forces acting on the bucket
When an object is being lowered or lifted by a rope, there are two main forces acting on it: the tension in the rope and the weight of the object. In this case, the tension in the rope is given as 181 N, and the weight of the bucket can be calculated using the mass and the acceleration due to gravity (9.8 m/s^2). The weight is given by the equation:
Weight = mass × acceleration due to gravity
Step 3: Calculate the weight of the bucket
Let's calculate the weight of the bucket using the given mass:
Weight = 14.0 kg × 9.8 m/s^2
Weight = 137.2 N
So, the weight of the bucket is 137.2 N.
Step 4: Apply Newton's second law of motion
Newton's second law of motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force acting on the bucket is equal to the tension in the rope (181 N) minus the weight of the bucket (137.2N). We can express this as an equation:
Net force = tension - weight
Step 5: Calculate the net force acting on the bucket
Let's calculate the net force using the tension and weight values we calculated:
Net force = 181 N - 137.2 N
Net force = 43.8 N
So, the net force acting on the bucket is 43.8 N.
Step 6: Calculate the acceleration
Now that we have the net force acting on the bucket, we can use Newton's second law of motion to find the acceleration. Rearranging the equation, we have:
Acceleration = Net force / Mass
Plugging in the values we calculated:
Acceleration = 43.8 N / 14.0 kg
Acceleration = 3.13 m/s^2
Therefore, the acceleration of the bucket is 3.13 m/s^2.