Problems 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52 describe a situation. For each, draw a motion diagram, a force-identification diagram, and a free-body diagram. A Styrofoam ball has just been shot straight up. Air resistance is not negligible.

Verified step by step guidance

1. Identify the object in motion and the forces acting on it. In this case, the object is a Styrofoam ball that has been shot straight up. The forces acting on it include gravity (downward force) and air resistance (also acting downward as the ball moves upward).
2. Draw the motion diagram. This diagram should show the ball at various points in its trajectory upwards and then downwards. Use dots to represent the position of the ball at equal time intervals. Arrows can be used to indicate the velocity of the ball at each point, which decreases as it moves up until it reaches the peak (where velocity is zero), and then increases as it moves down.
3. Create a force-identification diagram. This diagram should label the ball and clearly show all the forces acting on it. Label the force of gravity as 'F_g' pointing downward and the air resistance as 'F_{air}' also pointing downward.
4. Draw the free-body diagram. This diagram isolates the ball and represents only the forces acting upon it, without other distractions. Represent the forces with arrows starting from the center of the ball: a downward arrow for gravity and another downward arrow for air resistance, which might be smaller or larger depending on the specifics of the problem.
5. Analyze the diagrams to understand the motion of the ball. The motion diagram shows how the velocity changes, the force-identification diagram shows all the forces in play, and the free-body diagram helps in understanding how these forces interact to affect the motion of the ball.

Key Concepts

Motion Diagrams

A motion diagram visually represents the position of an object at various time intervals, illustrating its trajectory and changes in velocity. In the context of the Styrofoam ball shot upwards, the diagram will show the ball's ascent, peak, and descent, highlighting how its position changes over time due to the influence of forces acting on it.

Free-Body Diagrams

A free-body diagram is a graphical representation that shows all the forces acting on an object. For the Styrofoam ball, this diagram will include the force of gravity acting downward and the force of air resistance acting upward, allowing for a clear analysis of the net force and resulting motion of the ball as it moves through the air.

Air Resistance

Air resistance, or drag, is a force that opposes the motion of an object through the air. It is particularly significant for lightweight objects like a Styrofoam ball, as it affects the ball's acceleration and velocity during its flight. Understanding air resistance is crucial for accurately predicting the ball's motion and the forces acting on it.