The instruments attached to a weather balloon have a mass of 5.1 kg.
(a) The balloon is released and exerts an upward force of 102 N on the instruments. What is the acceleration of the balloon and instruments?
(b) After the balloon has accelerated for 13 seconds, the instruments are released. What is the velocity of the instruments at the moment of the their release?
(c) What net force acts on the instruments after their release?
(d) When does the direction of their velocity first become downward?
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To answer these questions, we need to apply Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration (F = ma). We also need to consider the forces acting on the balloon and instruments system.
(a) To find the acceleration of the balloon and instruments, we need to calculate the net force acting on the system and divide it by their combined mass.
Net force = Upward force exerted by the balloon - Weight force (mg)
The weight force can be calculated by multiplying the mass of the instruments (5.1 kg) by the acceleration due to gravity (9.8 m/s^2).
Weight force = 5.1 kg * 9.8 m/s^2
Now, subtract the weight force from the upward force exerted by the balloon.
Net force = 102 N - (5.1 kg * 9.8 m/s^2)
Finally, divide the net force by the combined mass (5.1 kg) to find the acceleration.
Acceleration = (102 N - (5.1 kg * 9.8 m/s^2)) / 5.1 kg
(b) After the instruments are released, their acceleration becomes zero since there are no external forces acting on them. Therefore, the velocity remains constant. To find the velocity at the moment of release, use the equation:
Velocity = Initial velocity + (Acceleration * Time)
Since the acceleration is zero, the velocity at the moment of release is simply the velocity at that time, which can be found by multiplying the acceleration calculated in part (a) by the time elapsed (13 seconds).
Velocity = Acceleration * Time
(c) After the instruments are released, they are no longer subject to the upward force of the balloon. The only force acting on them is the weight force due to gravity, which is equal to their mass multiplied by the acceleration due to gravity. Therefore, the net force acting on the instruments after their release is the weight force.
Net force = Mass of instruments * Acceleration due to gravity
(d) The direction of the velocity will become downward when the net force acting on the instruments becomes greater than zero, which occurs as soon as the weight force (downward) exceeds the remaining upward force. This will happen immediately after the instruments are released from the balloon.