A research balloon of total mass 445 kg is descending vertically with a downward acceleration of 1.3 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 1.5 m/s2, presuming that the upward lift of the balloon does not change.
To determine the amount of ballast that must be thrown from the car, we need to use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this scenario, the force acting on the balloon is the difference between the downward force due to gravity and the upward force due to the lift of the balloon. The downward force due to gravity is given by the formula: force = mass x acceleration due to gravity, where the mass is the total mass of the balloon and the car (445 kg) and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the downward force due to gravity is: 445 kg x 9.8 m/s^2 = 4361 N.
The upward force due to the lift of the balloon is not changing, so the net force required to give the balloon an upward acceleration of 1.5 m/s^2 can be calculated using the formula: net force = mass x upward acceleration. Rearranging the formula, we get: mass = net force / upward acceleration.
Substituting the values, we find: mass = 4361 N / 1.5 m/s^2 = 2907.3 kg.
Now, we need to determine the mass of the ballast that must be thrown from the car. This can be calculated by subtracting the mass of the balloon and the car from the total mass needed. Therefore, the mass of the ballast is: 2907.3 kg - 445 kg = 2462.3 kg.
Therefore, approximately 2462.3 kg of ballast must be thrown from the car to give the balloon an upward acceleration equal to 1.5 m/s^2, assuming the upward lift of the balloon does not change.