1.A hot air balloon is rising upwards at a constant velocity of 5m.s when the balloon is 100m above the ground, a sandbag is dropped from it. 1.1 what is the magnitude of the acceleration of:a)The hot-air balloon while the sandbag is in it.b)The sandbag the moment is dropped from the hot air balloon.
a,0
1.1 a). They say it is rising at constant velocity before the bag drops. That information contains your answer.
1.1 b) You need to provide more information, preferably the mass of the sandbag and the rest of the balloon.
The acceleration of the balloon at any time is Fnet/M. The drag force and buoyancy do not instanteously change but the weight force and the mass do change.
The new value of a (upward) is
Ms*g/(M - Ms)
= g/[(M/Ms) -1)]
Knowing the velocity before dropping won't tell you anything about M and Ms.
1.1 the balloon is rising upwards acceleration is always downwards so therefore the magnitude of acceleration is 9.8 ms^-2 downwards.
Alternatively at constant velocity, acceleration is 0 ms^-2 , which clearly indicates that the force is 0 newtons, so therefore the only acceleration that exist is gravitational acceleration
To find the magnitude of the acceleration in these scenarios, we need to analyze the forces acting on the objects involved.
a) The hot-air balloon while the sandbag is in it:
When the hot air balloon is rising upwards at a constant velocity, it means that the net force acting on it is zero. In this case, the upward buoyant force exerted by the hot air balloon is equal to the downward gravitational force acting on it (including the mass of the sandbag).
The magnitude of the acceleration in this case is zero since there is no change in velocity. The forces are balanced.
b) The sandbag the moment it is dropped from the hot air balloon:
When the sandbag is dropped from the hot air balloon, the only force acting on it is the force of gravity, which pulls objects towards the center of the Earth. This force leads to an acceleration known as the acceleration due to gravity.
The acceleration due to gravity is approximately 9.8 m/s² near the surface of the Earth. Therefore, the magnitude of the acceleration of the sandbag is approximately 9.8 m/s².
Note: The assumption here is that air resistance is negligible in both cases.