Several people are riding in a hot-air balloon. The combined mass of the people and balloon is 284 kg. The balloon is motionless in the air, because the downward-acting weight of the people and balloon is balanced by an upward-acting 'buoyant' force. If the buoyant force remains constant, how much mass should be dropped overboard so the balloon acquires an upward acceleration of 0.28 m/s2?
weight=ma
but m is the weight left
weight=(284-Weight)*.28m/s^2
solve for weight
but if you have two variables how do you solve? I understand that force=ma so the normal force is (284)(9.8)=2783.2, but I don't really understand how to determine when acceleration is .28
bois there is this guy called "Mr.Hojman" and he's answering questions with this "message" here it is....
Please don't cheat and use this website do your work and learn! - Mr.Hojman
To determine the mass that needs to be dropped overboard, we need to set up an equation based on Newton's second law of motion:
ΣF = m * a
Where:
ΣF is the net force acting on the system,
m is the mass of the system, and
a is the acceleration of the system.
In this case, the net force acting on the system is the difference between the buoyant force and the weight of the system:
ΣF = F_buoyant - Weight
The weight can be calculated using the formula:
Weight = mass * g
Where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the upward acceleration of the balloon is 0.28 m/s^2, we can rewrite the equation as:
F_buoyant - Weight = m * a
Substituting the values, we have:
F_buoyant - (mass * g) = mass * a
To solve for the mass to be dropped, rearrange the equation as:
mass = (F_buoyant - mass * g) / a
Given the combined mass of the people and balloon is 284 kg, and assuming the buoyant force remains constant, we can calculate the mass that needs to be dropped overboard using the equation above.