the instruments attached to a weather balloon have a mass of 5.0 kg. the balloon is released and exerts an upward force of 98 N on the instruments.
(a) what is the acceleration of the balloon and instruments? (answer is 9.8 m/s^2.. just don't know how to get there..)
(b)after the balloon has accelerated for 10.0 s, the intruments are released. What is the velocity of the instruments at the moment of their release?
(c) what net force acts on the instruments after their release?
(d) when does the direction of the instruments velocity first become downward?
To find the answers to the given questions, we can apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) To find the acceleration of the balloon and instruments, we can use the given information that the upward force exerted by the balloon is 98 N and the mass of the instruments is 5.0 kg. We can rearrange Newton's second law equation to solve for acceleration:
Net force = mass x acceleration
98 N = 5.0 kg x acceleration
Divide both sides by 5.0 kg:
acceleration = 98 N / 5.0 kg
acceleration = 19.6 m/s²
Note: The answer you've provided (9.8 m/s²) seems to be the acceleration due to gravity, which is the same when an object falls freely near the Earth's surface.
(b) After the balloon has accelerated for 10.0 s, the instruments are released. Since the instruments are released, we can assume that there are no external forces acting on them except for gravity. Therefore, the only force acting on the instruments is their weight.
Using the formula for calculate velocity under uniform acceleration:
Velocity = Initial velocity + (acceleration x time)
Since the instruments were released, their initial velocity would be considered zero:
Velocity = 0 + (19.6 m/s² x 10.0 s)
Velocity = 196 m/s
So, the velocity of the instruments at the moment of their release is 196 m/s.
(c) After the instruments are released, the only force acting on them is the force of gravity, which pulls them downward. The force of gravity can be calculated using the formula:
Force = mass x acceleration due to gravity
Force = 5.0 kg x 9.8 m/s²
Force = 49 N
Therefore, the net force acting on the instruments after their release is 49 N, directed downward.
(d) The direction of the instrument's velocity will start to become downward when the upward force of the balloon becomes equal to the instrument's weight. Since the weight of the instruments is 49 N, we can use this information to find the time when the direction of velocity becomes downward.
Net force = mass x acceleration
98 N - (5.0 kg x 9.8 m/s²) = 5.0 kg x acceleration
Simplifying the equation:
98 N - 49 N = 5.0 kg x acceleration
49 N = 5.0 kg x acceleration
acceleration = 49 N / 5.0 kg
acceleration = 9.8 m/s²
As we can see, at this point, the acceleration is equal to the acceleration due to gravity. The direction of the instrument's velocity will first become downward when the acceleration becomes 9.8 m/s².
Please let me know if I can help you with anything else.