The instruments attached to a balloon have a mass of 5kg. The balloon is released and exerts an upward force of 100 N. After the balloon has accelerated for 10s, the instruments are released. What is the velocity of the instruments at the moment of release?
I am wondering if "upward force" means net upward force, I assume so. weight is already in the number
vf=at=force/mass * time=100/5 * 10=20m/s
To calculate the velocity of the instruments at the moment of release, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
First, let's find the net force on the instruments after the balloon has accelerated for 10 seconds. The upward force exerted by the balloon is 100 N, and we know that the weight (force due to gravity) is acting downward. Therefore, the net force on the instruments can be calculated by subtracting the weight from the upward force.
Weight = mass × acceleration due to gravity
In this case, the mass of the instruments is 5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the instruments is:
Weight = 5 kg × 9.8 m/s^2 = 49 N
Now, to find the net force:
Net Force = Upward Force - Weight
= 100 N - 49 N
= 51 N
Since the instruments are released, the net force acting on them is equal to their mass multiplied by their acceleration:
Net Force = mass × acceleration
Rearranging the equation to solve for acceleration:
acceleration = Net Force / mass
= 51 N / 5 kg
= 10.2 m/s^2
Now that we have the acceleration, we can use the kinematic equation to find the velocity of the instruments at the moment of release:
velocity = initial velocity + acceleration × time
Since the instruments were released by the balloon, we can assume that their initial velocity is zero. Thus, the equation simplifies to:
velocity = acceleration × time
= 10.2 m/s^2 × 10 s
= 102 m/s
Therefore, the velocity of the instruments at the moment of release is 102 m/s.