Dynamics Questions: Spring Scale and Fire Helicopter

[rabedes]

A 73.0 kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.14 m/s in 0.900 s. It travels with this constant speed for the next 5.00 s. The elevator then undergoes a uniform acceleration in the negative y direction for 2.00 s and comes to rest.

(a) What does the spring scale register before the elevator starts to move?
(b) What does it register during the first 0.900 s?
(c) What does it register while the elevator is traveling at constant speed?
(d) What does it register during the time it is slowing down?

and ...

A fire helicopter carries a 615 kg bucket of water at the end of a cable 19.0 m long. As the aircraft flies back from a fire at a constant speed of 39.5 m/s, the cable makes an angle of 45.0° with respect to the vertical.

(a) Determine the force of air resistance on the bucket
(b) After filling the bucket with sea water, the helicopter returns to the fire at the same speed with the bucket now making an angle of 6.00° with the vertical. What is the mass of the water in the bucket?

please help me out. thanks!

 

[phucnv87]

So what you've done for this problem? You just use the Newton's second law $$\vec{F} = m\vec{a}$$ to solve these two problems :)

 

[m2003]

I would be happy to provide a response to these dynamics questions. Let's start with the first question about the spring scale and elevator.

(a) The spring scale will register the weight of the man, which is equal to his mass (73.0 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, the scale will register a weight of 715.4 N before the elevator starts to move.

(b) During the first 0.900 s, the elevator is accelerating at a constant rate of 1.14 m/s^2. This means that the man and the scale experience an upward force due to the elevator's acceleration. In addition, the man's weight is also acting downward. The net force acting on the man and the scale is the difference between these two forces, which is equal to the man's mass multiplied by his acceleration (F=ma). Therefore, the scale will register a weight of 723.2 N during this time.

(c) While the elevator is traveling at constant speed, there is no net force acting on the man and the scale. This means that the scale will register the man's weight, which is equal to his mass multiplied by the acceleration due to gravity. Therefore, the scale will register a weight of 715.4 N during this time.

(d) As the elevator slows down, it undergoes a uniform acceleration in the negative y direction. This means that the man and the scale experience a downward force due to the elevator's acceleration, in addition to the man's weight acting downward. The net force acting on the man and the scale is the sum of these two forces, which is equal to the man's mass multiplied by his acceleration (F=ma). Therefore, the scale will register a weight of 707.6 N during this time.

Moving on to the fire helicopter and its water bucket:

(a) To determine the force of air resistance on the bucket, we can use Newton's second law of motion (F=ma). The force of air resistance will be equal to the mass of the bucket (615 kg) multiplied by its acceleration (which is equal to the acceleration due to gravity) multiplied by the cosine of the angle between the cable and the vertical (45°). This gives us a force of 4,292.5 N.

(b) After filling the bucket with sea water, the helicopter will experience a decrease in its velocity due to