Question

If the net force on a hot-air balloon is directed straight upward, which way does the acceleration point?
A) downward
B) upward
C) upward only if the balloon is rising
D) the same direction as the force of gravity

Answer 1

Hint: Newton’s second law relates the direction of the net force of a body with its acceleration. The direction of the force is in the direction of the net acceleration that is produced in the object.

Formula used: In this solution we will be using the following formula,
Newton’s second law $\vec F = m\vec a$ where $\vec F$ is the force acting on a body of mass $m$ causing an acceleration $\vec a$.

Complete step by step solution:
We’ve been given that the net force on a hot-air balloon is directed straight upwards. Using Newton’s second law of motion, we can write
$\Rightarrow\vec F = m\vec a$
In the above equation, for the left side to be equal to the right side, the vector of force and acceleration must have the same direction. So, the direction of the acceleration must also be equal to the direction of the force i.e. in the straight upward direction. If the balloon was moving downwards, the net direction of the force will also be downwards. Hence the correct choice is option (C) since the force is upwards only if the balloon is rising.

Note:
Option (B) can be ruled out because the net force on the balloon can be in the downward direction if the balloon is moving upwards but is slowing down and will eventually move downwards. The balloon has to be rising for the net force to be in the upward direction. Option (D) is not correct because the hot-air balloon produces a greater force in the upwards direction when it rises by using lightweight gases and hence it overcomes the gravitational force. So, the net direction of the force would then be in the upwards direction which is again the direction of motion in the case.