For kinematics, what is an example of gravitational force being negative and one where it is positive? Explain the difference.
In the context of kinematics, the gravitational force can be both positive and negative, depending on the direction in which it acts. To understand this, let's consider two examples: an object being thrown upwards and an object being thrown downwards.
1. Example with Negative Gravitational Force:
Suppose you throw a ball straight upwards. In this case, the gravitational force acts in the downward direction (opposite to the ball's motion). As a result, the gravitational force is taken as negative because it opposes the ball's motion. The ball accelerates downward due to gravity, eventually coming to a stop at its highest point before falling back down.
2. Example with Positive Gravitational Force:
Now consider throwing the same ball straight downwards. In this scenario, the gravitational force acts in the same direction as the ball's motion, pulling it downward. Here, the gravitational force is considered positive because it aids the ball's motion. The ball accelerates further as it falls and eventually increases its speed due to the gravitational force.
The key difference is that the sign (+/-) of the gravitational force indicates its direction relative to the object's motion. When the gravitational force opposes motion, it is typically taken as negative. Conversely, when the gravitational force assists motion, it is usually considered positive.