A 4.504.504.50-kg experimental cart undergoes an acceleration in a straight line (the xxx-axis). The graph in Fig. E4.134.134.13 shows this acceleration as a function of time. During what times is the net force on the cart a constant?

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 15th Edition

Ch 04: Newton's Laws of Motion

Problem 13b

Chapter 4, Problem 13b

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?

Verified step by step guidance

Step 1: Analyze the graph provided. The acceleration (a) is plotted as a function of time (t). The graph shows regions where the acceleration is constant, which corresponds to a constant net force on the cart. According to Newton's second law, the net force (F) is given by F = m * a, where m is the mass of the cart and a is the acceleration.

Step 2: Identify the regions of constant acceleration from the graph. In the first graph, the acceleration is constant between 2 ms and 6 ms (a = 2 m/s²). In the second graph, the acceleration is constant between 2 s and 4 s (a = 10 m/s²). These intervals indicate that the net force is constant during these times.

Step 3: Recall that when acceleration changes (either increasing or decreasing), the net force is not constant. For example, in the first graph, the acceleration decreases from 6 m/s² to 2 m/s² between 0 ms and 2 ms, and decreases again from 2 m/s² to 0 m/s² between 8 ms and 12 ms. Similarly, in the second graph, the acceleration increases and decreases outside the interval of constant acceleration.

Step 4: Use Newton's second law to confirm the relationship between force and acceleration. Since the mass of the cart is constant (4.50 kg), the net force is directly proportional to the acceleration. Therefore, during the intervals of constant acceleration, the net force remains constant.

Step 5: Summarize the findings. The net force on the cart is constant during the intervals where the acceleration is constant: 2 ms to 6 ms in the first graph, and 2 s to 4 s in the second graph. Outside these intervals, the net force varies due to changes in acceleration.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 analyzing the forces acting on the experimental cart as it accelerates.

Acceleration

Acceleration is defined as the rate of change of velocity of an object with respect to time. It can be constant or variable, and in this context, it is represented as a function of time in the provided graph. The graph shows how acceleration changes, which helps determine when the net force on the cart remains constant, as constant acceleration indicates a constant net force.

Graph Interpretation

Interpreting graphs is essential in physics for understanding relationships between variables. In this case, the graph depicts acceleration (y-axis) as a function of time (x-axis). By analyzing the graph, one can identify intervals where the acceleration is constant, which corresponds to periods where the net force acting on the cart is also constant, as per Newton's Second Law.

Recommended video:

Guided course

07:32

Graphing Position, Velocity, and Acceleration Graphs

Related Practice

Textbook Question

A hockey puck with mass $0.160$ kg is at rest at the origin ( $x = 0$ ) on the horizontal, frictionless surface of the rink. At time $t = 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$ -axis; she continues to apply this force until $t = 2.00$ s. If the same force is again applied at $t equals 5.00$ s, what are the position and speed of the puck at $t equals 7.00$ s?

views

Textbook Question

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g equals 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What is the watermelon's mass on the earth's surface?

views

rank

Textbook Question

A small $8.00$ -kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation $F = A + B t^{2}$ . Measurements show that at $t equals 0$ , the force is $100.0$ N, and at the end of the first $2.00$ s, it is $150.0$ N. Find the constants $A$ and $B$ , including their SI units.

views

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. Find the maximum net force on this cart. When does this maximum force occur?

views

Textbook Question

An astronaut's pack weighs $17.5$ N when she is on the earth but only $3.24$ N when she is at the surface of a moon. What is the acceleration due to gravity on this moon?

views

Textbook Question

A hockey puck with mass $0.160$ kg is at rest at the origin ( $x equals 0$ ) on the horizontal, frictionless surface of the rink. At time $t equals 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$ -axis; she continues to apply this force until $t equals 2.00$ s. What are the position and speed of the puck at $t equals 2.00$ s?

views