Final answer:
The displacement of the bucket can be calculated using the equation s = ut + 0.5at^2. The work done by each force can be calculated using the equation W = F x d x cos(theta). The net force acting on the bucket can be calculated using Newton's second law.
Step-by-step explanation:
(a) To calculate the displacement of the bucket, we can use the equation:
s = ut + 0.5at^2
where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Given that the bucket starts from rest, the initial velocity (u) is 0 m/s.
Plugging in the values, we get:
s = 0(3.0) + 0.5(2.2)(3.0)^2 = 9.9 m
Therefore, the displacement of the bucket is 9.9 meters.
(b) To calculate the work done by each force, we can use the equation:
W = F x d x cos(theta)
where W is the work done, F is the force, d is the displacement, and theta is the angle between the force and displacement.
- The work done by the rope pulling force is:
W_rope = F_rope x d x cos(0) = F_rope x d
- The work done by the gravitational force is:
W_gravity = F_gravity x d x cos(180) = -F_gravity x d
- The work done by friction is:
W_friction = F_friction x d x cos(180) = -F_friction x d
(c) The total mechanical work done on the bucket is the sum of the work done by each force:
Total work = W_rope + W_gravity + W_friction
(d) The net force acting on the bucket can be calculated using Newton's second law:
F_net = m x a
where F_net is the net force, m is the mass, and a is the acceleration.
Plugging in the values, we get:
F_net = 2.0 kg x 2.2 m/s^2 = 4.4 N
The work done by the net force can be calculated using the equation:
W_net = F_net x d x cos(theta)
Since the acceleration is in the same direction as the displacement, the angle between the force and displacement is 0 degrees.
Therefore, the work done by the net force is:
W_net = F_net x d
We can compare this value to the total mechanical work done on the bucket calculated in (c) to see if they are equal.