A 4.504.50-kg experimental cart undergoes an acceleration in a straight line (the xx-axis). The graph in Fig. E4.134.13 shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 04: Newton's Laws of Motion

Problem 13a

Chapter 4, Problem 13a

A $4.50$ -kg experimental cart undergoes an acceleration in a straight line (the $x$ -axis). The graph in Fig. E $4.13$ shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

Verified step by step guidance

Step 1: Identify the relationship between force and acceleration using Newton's Second Law, which states that the net force on an object is given by $ F = ma $, where $ F $ is the net force, $ m $ is the mass, and $ a $ is the acceleration.

Step 2: From the graph provided, determine the maximum acceleration value. In the first graph, the maximum acceleration is $ 6.0 \, \text{m/s}^2 $ at $ t = 2.0 \, \text{ms} $.

Step 3: Use the given mass of the cart, $ m = 4.50 \, \text{kg} $, and substitute the maximum acceleration value into the formula $ F = ma $ to calculate the maximum net force.

Step 4: Note that the maximum force occurs at the time corresponding to the maximum acceleration, which is $ t = 2.0 \, \text{ms} $.

Step 5: Ensure units are consistent throughout the calculation. Convert $ t $ from milliseconds to seconds if necessary, and express the final force in $ \text{N} $ (Newtons).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. Understanding this law is crucial for determining the net force acting on the cart based on its acceleration.

Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. It can be constant or variable, as shown in the provided graph, which depicts acceleration as a function of time. The maximum acceleration value from the graph indicates the point at which the net force on the cart is also maximized, as per Newton's Second Law.

Graph Interpretation

Interpreting graphs is essential in physics for understanding how different quantities relate to each other over time. In this case, the graph shows acceleration versus time, allowing us to identify key features such as maximum acceleration and the duration of that acceleration. This information is vital for calculating the maximum net force and determining when it occurs.

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Textbook Question

A $4.50$ -kg experimental cart undergoes an acceleration in a straight line (the $x$ -axis). The graph in Fig. E $4.13$ shows this acceleration as a function of time. During what times is the net force on the cart a constant?

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Textbook Question

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