A box of bananas weighing 40.0 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.400.40, and the coefficient of kinetic friction is 0.200.20. If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it?

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 05: Applying Newton's Laws

Problem 28a

Chapter 5, Problem 28a

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?

Verified step by step guidance

Step 1: Understand the problem. The box is at rest, meaning there is no horizontal force applied to it. The friction force in this case will be static friction, which opposes any potential motion but does not exceed the maximum static friction force.

Step 2: Recall the formula for static friction: $ f_s \leq \mu_s \cdot F_N $, where $ \mu_s $ is the coefficient of static friction and $ F_N $ is the normal force. The normal force for an object resting on a horizontal surface is equal to its weight.

Step 3: Substitute the given values into the formula. The weight of the box is $ F_N = 40.0 \, \text{N} $, and the coefficient of static friction is $ \mu_s = 0.40 $. Calculate the maximum static friction force: $ f_{s, \text{max}} = \mu_s \cdot F_N $.

Step 4: Since no horizontal force is applied, the box remains at rest. The actual static friction force $ f_s $ will be equal to the force trying to move the box, which in this case is zero. Therefore, $ f_s = 0 \, \text{N} $.

Step 5: Conclude that the friction force exerted on the box is $ 0 \, \text{N} $ because there is no applied force attempting to move the box.

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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 prevents an object from starting to move when a horizontal force is applied. It acts in the opposite direction to the applied force and varies in magnitude up to a maximum value, which is determined by the coefficient of static friction and the normal force. In this case, since no horizontal force is applied, the static friction force is zero.

Normal Force

The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. It acts upward against the weight of the object, which in this scenario is the weight of the box of bananas. The normal force is equal to the weight of the box when it is on a horizontal surface, thus it is 40.0 N in this case.

Friction Force

Friction force is the resistive force that opposes the relative motion of two surfaces in contact. It can be static or kinetic, depending on whether the object is at rest or in motion. Since the box is at rest and no external horizontal force is applied, the friction force exerted on the box is zero, as there is no need to counteract any applied force.

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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 keep the box moving at constant velocity once it has been started?

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

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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Textbook Question

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?

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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