Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 05: Applying Newton's Laws

Problem 26a

Chapter 5, Problem 26a

In a laboratory experiment on friction, a $135$ -N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to increase thereafter. Figure E $5.26$ shows a graph of the friction force on this block as a function of the pull. Identify the regions of the graph where static friction and kinetic friction occur.

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Examine the graph provided. The x-axis represents the applied force (F) in Newtons, and the y-axis represents the frictional force (f) in Newtons. The graph shows a red line that increases linearly, peaks, and then becomes constant.

Identify the region of static friction. Static friction occurs when the block is stationary and resists the applied force. In the graph, this is the region where the frictional force increases linearly with the applied force, up to the peak at approximately 40 N.

Determine the transition point. The peak of the graph (around 40 N) represents the maximum static friction force, also known as the limiting friction. Beyond this point, the block begins to move, and static friction transitions to kinetic friction.

Identify the region of kinetic friction. Kinetic friction occurs once the block is in motion. In the graph, this is the region where the frictional force becomes constant (approximately 20 N) after the peak.

Summarize the behavior. Static friction resists motion and increases with the applied force until the maximum static friction is reached. Once the block starts moving, kinetic friction takes over, which is typically lower and remains constant regardless of the applied force.

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Key Concepts

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

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It acts when an object is at rest and is being pulled but has not yet started to move. The maximum static friction force increases with the applied force until it reaches a threshold, beyond which the object begins to slide.

Kinetic Friction

Kinetic friction, also known as dynamic friction, is the force that opposes the motion of two surfaces sliding past each other. Once the object starts moving, the frictional force decreases to a constant value, which is typically lower than the maximum static friction. This force remains relatively constant regardless of the speed of the sliding object.

Friction Force Graph

A friction force graph plots the frictional force against the applied pull force. In the graph, the initial slope represents static friction, which increases until it reaches a peak. After the object starts moving, the graph levels off, indicating the constant kinetic friction force. Understanding this graph helps identify the transition point between static and kinetic friction.

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Related Practice

Textbook Question

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. In terms of this jumper's weight w, what force does the ground exert on him or her during the jump?

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Textbook Question

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$ , and the coefficient of kinetic friction is $0.20$ . What minimum horizontal force must the monkey apply to start the box in motion?

A $5.00$ -kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force $F (t)$ is applied to the end of the rope, and the height of the crate above its initial position is given by $y (t) =$ ( $2.80$ m/s)t + ( $0.610$ m/s³)t³. What is the magnitude of $F$ when $t equals 4.00$ s?

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Textbook Question

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$ , and the coefficient of kinetic friction is $0.20$ . If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it?

A $2.00$ -kg box is moving to the right with speed $9.00$ m/s on a horizontal, frictionless surface. At $t equals 0$ a horizontal force is applied to the box. The force is directed to the left and has magnitude $F (t) =$ ( $6.00$ N/s²)t². What distance does the box move from its position at $t equals 0$ before its speed is reduced to zero?

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Textbook Question

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$ , and the coefficient of kinetic friction is $0.20$ . What is the magnitude of the friction force if a monkey applies a horizontal force of $6.0$ N to the box and the box is initially at rest?

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