A single force with x-component Fₓ acts on a 500 g object as it moves along the x-axis. The object's acceleration graph aₓ versus t) is shown in FIGURE P5.30. Draw a graph of Fₓ versus t.

Verified step by step guidance

1. Step 1: Understand the relationship between force and acceleration. According to Newton's second law, the force acting on an object is given by \( F_x = m \cdot a_x \), where \( m \) is the mass of the object and \( a_x \) is its acceleration.
2. Step 2: Convert the mass of the object into kilograms, as the SI unit for mass is kilograms. The given mass is 500 g, so \( m = 500 \, \text{g} = 0.500 \, \text{kg} \).
3. Step 3: Analyze the acceleration graph \( a_x \) versus \( t \). Identify the values of \( a_x \) at different points in time \( t \) from the graph. These values will be used to calculate the force \( F_x \) at corresponding times.
4. Step 4: Use the formula \( F_x = m \cdot a_x \) to calculate the force at each time point. Multiply the mass \( m = 0.500 \, \text{kg} \) by the acceleration \( a_x \) values obtained from the graph.
5. Step 5: Plot the calculated \( F_x \) values against time \( t \) to create the graph of \( F_x \) versus \( t \). Ensure the graph reflects the same trends and features as the acceleration graph, scaled by the mass.

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is fundamental for understanding how forces affect the motion of an object. In this scenario, knowing the mass of the object and its acceleration allows us to calculate the force acting on it at any given time.

Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. It can be positive (speeding up), negative (slowing down), or zero (constant velocity). The acceleration graph provided in the question indicates how the object's acceleration varies over time, which is crucial for determining the corresponding force acting on the object.

Graphing Force vs. Time

Graphing force versus time involves plotting the calculated force values against time intervals. Since force is directly proportional to acceleration (as per Newton's Second Law), the shape of the force graph will mirror the acceleration graph, scaled by the object's mass. This visual representation helps in understanding how the force changes as the object's acceleration varies over time.