Ch 05: Force and Motion

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 05: Force and Motion

Problem 38a

Chapter 5, Problem 38a

Problems 35, 36, 37, 38, 39, and 40 show a free-body diagram. For each: Identify the direction of the acceleration vector a and show it as a vector next to your diagram. Or, if appropriate, write a = 0.

Verified step by step guidance

Step 1: Analyze the forces in the diagram. The forces shown are: the normal force (n) pointing upward along the y-axis, the gravitational force (Fg) pointing downward along the y-axis, the kinetic friction force (fk) pointing left along the x-axis, and the net force (Fnet) pointing right along the x-axis.

Step 2: Determine the net force in the y-direction. The normal force (n) and gravitational force (Fg) are equal in magnitude but opposite in direction, so they cancel each other out. This means there is no acceleration in the y-direction (a_y = 0).

Step 3: Determine the net force in the x-direction. The net force (Fnet) is pointing to the right, while the kinetic friction force (fk) is pointing to the left. Since Fnet is explicitly labeled, it indicates that the object is accelerating to the right along the x-axis.

Step 4: Conclude the direction of the acceleration vector. Since there is no acceleration in the y-direction and the object is accelerating to the right in the x-direction, the acceleration vector (a) points to the right along the x-axis.

Step 5: Represent the acceleration vector on the diagram. Draw a vector labeled 'a' pointing to the right along the x-axis next to the diagram to indicate the direction of acceleration.

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Key Concepts

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

Free-Body Diagram

A free-body diagram is a graphical representation used to visualize the forces acting on an object. It shows all the external forces, including their magnitudes and directions, allowing for a clear analysis of the net force and resulting motion. In this context, the diagram illustrates forces such as normal force (n), kinetic friction (fk), and gravitational force (Fg).

Net Force

The net force is the vector sum of all the forces acting on an object. It determines the object's acceleration according to Newton's second law, F_net = ma, where F_net is the net force, m is mass, and a is acceleration. In the provided diagram, the direction of the net force (F_net) indicates the overall influence of the forces on the object's motion.

Acceleration Vector

The acceleration vector represents the rate of change of velocity of an object and is directed in the same direction as the net force acting on it. If the net force is zero, the acceleration is also zero (a = 0), indicating that the object is either at rest or moving with constant velocity. Understanding the relationship between net force and acceleration is crucial for analyzing motion in physics.

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Related Practice

Textbook Question

A single force with x-component Fₓ acts on a 2.0 kg object as it moves along the x-axis. A graph of Fₓ versus t is shown in FIGURE P5.32. Draw an acceleration graph aₓ versus t) for this object.

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Textbook Question

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 model rocket is fired straight down from the top of a tower.

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Textbook Question

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if The force is halved and the object's mass is doubled?

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Textbook Question

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 rocket is being launched straight up. Air resistance is not negligible.

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Textbook Question

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.

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Textbook Question

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if the force is halved?

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