a 5 kg bucket is lowered by a rope in which there is 30 N of tension. What is the acceleration of the bucket?
acceleration=force/mass
To find the acceleration of the bucket, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
In this case, the net force acting on the bucket is the difference between the gravitational force pulling the bucket downward and the tension force pulling the bucket upward:
Net force = gravitational force - tension force.
The gravitational force can be calculated using the equation:
Gravitational force = mass × acceleration due to gravity.
Given that the mass of the bucket is 5 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the gravitational force:
Gravitational force = 5 kg × 9.8 m/s² = 49 N.
Now, we can calculate the net force:
Net force = gravitational force - tension force = 49 N - 30 N = 19 N.
Finally, we can use Newton's second law to find the acceleration:
Net force = mass × acceleration.
19 N = 5 kg × acceleration.
Solving for the acceleration:
acceleration = 19 N / 5 kg = 3.8 m/s².
Therefore, the acceleration of the bucket is 3.8 m/s².