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 solve this problem, we will need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force exerted on it and inversely proportional to its mass. Additionally, we will also need to consider the force of gravity acting on the instruments.
(a) To find the acceleration of the balloon and instruments, we need to calculate the net force acting on them. The net force is the difference between the upward force exerted by the balloon and the downward force of gravity. The force of gravity can be calculated using the formula F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the net force is given by:
Net Force = Upward Force - Downward Force
= 98 N - (5.0 kg * 9.8 m/s^2)
= 98 N - 49 N
= 49 N
Since we know that force equals mass times acceleration (F = m * a), we can rearrange the formula to solve for acceleration:
Acceleration = Net Force / Mass
= 49 N / 5.0 kg
= 9.8 m/s^2
Therefore, the acceleration of the balloon and instruments is 9.8 m/s^2.
(b) After 10.0 s of acceleration, the instruments are released. At this time, the balloon no longer exerts an upward force on them. The velocity of the instruments at the moment of release can be found using the formula v = a * t, where v is the velocity, a is the acceleration, and t is the time.
So, the velocity of the instruments at the moment of release is:
Velocity = Acceleration * Time
= 9.8 m/s^2 * 10.0 s
= 98 m/s
Therefore, the velocity of the instruments at the moment of their release is 98 m/s.
(c) After the instruments are released, the only force acting on them is the force of gravity. The net force acting on the instruments is simply the force of gravity, which is equal to their weight. The weight can be calculated using the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the net force acting on the instruments after their release is:
Net Force = Weight = Mass * Acceleration due to gravity
= 5.0 kg * 9.8 m/s^2
= 49 N
Therefore, the net force acting on the instruments after their release is 49 N.
(d) The direction of the instruments' velocity first becomes downward when their velocity becomes negative. Since the instruments were initially moving upward with a positive velocity, the point at which the velocity becomes negative indicates the change in direction.
To find when this occurs, we can use the formula v = u + a * t, where v is the final velocity (which is 0 m/s when the direction changes), u is the initial velocity (which is 98 m/s upward), a is the acceleration (which is -9.8 m/s^2 due to gravity), and t is the time.
Using this formula and solving for the time t:
0 m/s = 98 m/s + (-9.8 m/s^2) * t
Rearranging the equation:
-98 m/s = -9.8 m/s^2 * t
Dividing both sides by -9.8 m/s^2:
t = -98 m/s / -9.8 m/s^2
t = 10.0 s
Therefore, the direction of the instruments' velocity first becomes downward after 10.0 seconds.
To find the answers, we'll use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration. Let's solve each part step by step:
(a) To find the acceleration of the balloon and instruments, we can use the formula:
Force = mass * acceleration
Rearranging the formula to solve for acceleration gives us:
acceleration = Force / mass
Substituting the given values:
acceleration = 98 N / 5.0 kg = 19.6 m/s^2
However, the question asks for the acceleration of the balloon and instruments, so we need to take into account that the instruments have a mass of 5.0 kg as well. Therefore, the combined mass is 2 * 5.0 kg = 10 kg.
acceleration = 98 N / 10 kg = 9.8 m/s^2
Therefore, the acceleration of the balloon and instruments is 9.8 m/s^2.
(b) After the balloon has accelerated for 10.0 seconds, the instruments are released. The velocity of the instruments at the moment of their release can be found using the formula:
velocity = initial velocity + acceleration * time
Since the instruments were initially at rest, the initial velocity is 0 m/s. Plugging in the values:
velocity = 0 m/s + (9.8 m/s^2) * (10.0 s) = 98 m/s
Therefore, the velocity of the instruments at the moment of their release is 98 m/s.
(c) After the instruments are released, no net force acts on them. This is because the force exerted by the balloon is no longer present, and there are no other forces specified. Therefore, the net force acting on the instruments after their release is 0 N.
(d) The direction of the instruments' velocity first becomes downward when the magnitude of the force of gravity acting on them is greater than the upward force previously exerted by the balloon. This happens when the weight of the instruments exceeds 98 N.
Since weight is equal to mass multiplied by the acceleration due to gravity (which is approximately 9.8 m/s^2), we can find the weight of the instruments:
Weight = mass * acceleration due to gravity
Weight = 5.0 kg * 9.8 m/s^2 = 49 N
Therefore, the direction of the instruments' velocity first becomes downward when their weight equals or exceeds 49 N.