The instruments attached to a weather balloon have a mass of 5.2 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?
B) after the balloon has accelerated for 10s, the instruments are released. What is. The velocity of the instruments at the moment of their release?
C) when does the direction of their velocity first become downward?
A) Note that the weight W = 51N also acts on the instruments
a = [F(instr)-W]/M(instrmnt)
= (98- 51)/5.2 = 9.03 m/s^2
B) V = a*t , with t = 10 s
C) when g*t' = V of part B
Solve for t' (measured from release)
A) Well, to calculate the acceleration, we can use Newton's second law: F = m * a.
Given that the upward force is 98 N and the mass is 5.2 kg, we can rearrange the formula to solve for acceleration:
a = F / m
Plugging in the values, we get: a = 98 N / 5.2 kg ≈ 18.85 m/s².
B) If the instruments are released after 10 seconds, then we need to find the velocity achieved during that time. We can use another well-known formula: v = u + a * t, where u is the initial velocity, a is the acceleration, and t is the time.
Since the instruments start from rest, u = 0. Plugging in the values, we get: v = 0 + (18.85 m/s² * 10 s) ≈ 188.5 m/s.
C) The direction of the velocity becomes downward once the instruments are free from the balloon's influence. Given that the balloon is exerting an upward force, it means the instruments are counteracting that force in order to be released. So, the direction becomes downward as soon as they break free, which is at the moment of their release.
A) To determine the acceleration of the balloon and instruments, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force acting on the balloon and instruments is the upward force exerted by the balloon.
The net force is given as 98 N, and the mass of the balloon and instruments is 5.2 kg. Therefore, we can use the formula:
F = ma
Rearranging the formula to solve for acceleration (a), we get:
a = F/m
Substituting the given values, we have:
a = 98 N / 5.2 kg = 18.846 m/s^2 (approximately)
Therefore, the acceleration of the balloon and instruments is approximately 18.846 m/s^2.
B) After the balloon has accelerated for 10 seconds, the instruments are released. Assuming no additional external forces act upon the instruments after their release, we can use the formula for acceleration:
a = Δv / Δt
Rearranging the formula to solve for Δv (change in velocity), we get:
Δv = a * Δt
Substituting the given values, where a = 18.846 m/s^2 and Δt = 10 s, we have:
Δv = 18.846 m/s^2 * 10 s = 188.46 m/s (approximately)
Therefore, the velocity of the instruments at the moment of their release is approximately 188.46 m/s.
C) The direction of the instruments' velocity first becomes downward when their velocity changes from upward to downward. Since the instruments are released after accelerating for 10 seconds, their velocity will continue to increase in the upward direction until that point.
Therefore, the direction of the instruments' velocity first becomes downward after they are released, assuming no external forces act upon them to cause an immediate change in direction.
A) To find the acceleration of the balloon and instruments, we can use 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. The net force in this case is the difference between the upward force exerted by the balloon and the downward force due to the gravitational pull.
1. Calculate the gravitational force acting on the instruments:
The formula for gravitational force is 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).
F = 5.2 kg * 9.8 m/s^2 = 50.96 N
2. Calculate the net force:
Net force = upward force - downward force
Net force = 98 N - 50.96 N = 47.04 N
3. Calculate the acceleration:
Using Newton's second law, F = m * a, we rearrange the formula to solve for acceleration, a:
a = F / m
a = 47.04 N / 5.2 kg
a ≈ 9.06 m/s^2
Therefore, the acceleration of the balloon and instruments is approximately 9.06 m/s^2.
B) To find the velocity of the instruments at the moment of their release, we can use the concept of average velocity. Average velocity is the change in displacement divided by the time it takes.
1. Calculate the change in displacement:
The displacement is given by the formula d = v0 * t + (1/2) * a * t^2, where v0 is the initial velocity, t is the time, and a is the acceleration. In this case, the initial velocity is 0 m/s (since the instruments were released).
Substituting the values:
d = 0 * 10 s + (1/2) * 9.06 m/s^2 * (10 s)^2
d = 0 + 0.5 * 9.06 m/s^2 * 100 s^2
d ≈ 453 m
2. Calculate the velocity:
Velocity = displacement / time
Velocity = 453 m / 10 s
Velocity = 45.3 m/s
Therefore, the velocity of the instruments at the moment of their release is approximately 45.3 m/s.
C) To determine when the direction of the velocity first becomes downward, we need to find the time at which the instruments start moving downward. Since the velocity changes from upward to downward, we can assume that the initial velocity is positive (upward).
1. Calculate the time when the velocity changes direction:
Using the formula vf = vi + a * t, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Substituting the values:
0 m/s = 45.3 m/s + (-9.06 m/s^2) * t
Simplifying the equation:
-45.3 m/s = -9.06 m/s^2 * t
Dividing both sides by -9.06 m/s^2:
t ≈ 5 s
Therefore, the direction of their velocity first becomes downward approximately 5 seconds after releasing the instruments.