I found the first three parts of the question but I can't figure out part d.
The instruments attached to a weather balloon in the figure below have a mass(m) of 5.5 kg. The balloon is released and exerts an upward force(F) of 109 N on the instruments.
(a) What is the acceleration of the balloon and instruments?
10.02m/s^2
(b) After the balloon has accelerated for 10 s, the instruments are released. What is the velocity of the instruments at the moment of their release?
100.2 m/s
(c) What net force acts on the instruments after their release?
53.9N
(d) When does the direction of the instrument's velocity first become downward?
This is the one I can't figure out
how did you get the first three answers?
direction of velocity is downward at maximum height, and net velocity is zero.
vf=0=vi+at=100.2m/s-g*t
solve for t. This time is seconds after the acceleration of 10s
I don't understand this formula?
these are the two answers I got...
10
or
10.22
To determine when the direction of the instrument's velocity first becomes downward, we need to analyze the forces acting on the instruments after their release.
Initially, the balloon and instruments are moving upward with an acceleration of 10.02 m/s^2. This means that the net force acting on the system (balloon + instruments) is the difference between the weight of the system and the buoyant force on the balloon.
The weight of the system is given by the mass multiplied by the acceleration due to gravity (9.8 m/s^2):
Weight = mass * acceleration due to gravity
= 5.5 kg * 9.8 m/s^2
= 53.9 N
The buoyant force exerted by the atmosphere on the balloon is equal to the weight of the surrounding air displaced by the balloon. Since the balloon is moving upward with a constant velocity, the buoyant force must be equal to the weight of the system:
Buoyant force = Weight
= 53.9 N
Therefore, the net force acting on the instruments after their release is equal to zero (since the buoyant force and weight cancel each other out).
Since there is no net force acting on the instruments after their release, their velocity will remain constant until gravity starts to slow them down and eventually reverse their direction. This occurs when the gravitational force exceeds the buoyant force.
To find the moment when the direction of the instrument's velocity first becomes downward, we need to calculate the gravitational force acting on the instruments after their release.
Gravitational force = Weight of the instruments
= mass * acceleration due to gravity
= 5.5 kg * 9.8 m/s^2
= 53.9 N
Since the gravitational force is equal to the weight of the instruments, it is greater than the buoyant force, resulting in a downward net force on the instruments.
Therefore, the direction of the instrument's velocity first becomes downward as soon as they are released from the balloon.