A rope pulls a 2.0 kg bucket straight up, accelerating it from rest at 2.2 m/s2
for 3.0 seconds.
a) Calculate the displacement of the bucket.
b) Calculate the work done by each force acting on the bucket.
c) Calculate the total mechanical work done on the bucket.
d) Calculate the net force acting on the bucket and the work done by the net force. Compare your
answer to the total mechanical work done on the bucket as calculated in part c).
a) To calculate the displacement of the bucket, we use the equation:
displacement = initial velocity * time + 0.5 * acceleration * time^2
The initial velocity is 0 m/s since the bucket starts from rest. The acceleration is 2.2 m/s^2 and the time is 3.0 seconds. Plugging in the values, we get:
displacement = (0 * 3) + (0.5 * 2.2 * (3^2))
displacement = 0 + (0.5 * 2.2 * 9)
displacement = 0 + 9.9
displacement = 9.9 meters
b) The work done by a force is given by the equation:
work = force * distance * cos(theta)
where force is the magnitude of the force, distance is the displacement, and theta is the angle between the force and displacement vectors. In this case, the only force acting on the bucket is the tension force in the rope, and it acts in the same direction as the displacement. Therefore, theta is 0 degrees and cos(theta) is 1. The tension force can be calculated using Newton's second law:
force = mass * acceleration
force = 2.0 kg * 2.2 m/s^2
force = 4.4 N
Using this, we can calculate the work done by the tension force:
work_tension = 4.4 N * 9.9 m * 1
work_tension = 43.56 J
c) The total mechanical work done on the bucket is equal to the work done by all forces. In this case, it is only the work done by the tension force, so the total mechanical work is equal to the work done by the tension force:
work_total = work_tension = 43.56 J
d) The net force acting on the bucket is equal to the tension force since it is the only force acting on the bucket. The work done by the net force is also equal to the work done by the tension force, so the net force and work done by the net force are both equal to 43.56 N. This is the same as the total mechanical work done on the bucket, as calculated in part c).