A box of bananas weighing 40.0 40.040.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.400.400.40, and the coefficient of kinetic friction is 0.200.200.20. What minimum horizontal force must the monkey apply to start the box in motion?

Determine the maximum static friction force using the formula: fs=μsN, where μs is the coefficient of static friction and N is the normal force. Since the box is on a horizontal surface and there is no vertical motion, the normal force N is equal to the weight of the box, which is 40.0 N. Substitute the values into the static friction formula: fs=0.40×40.0. This gives the maximum static friction force. The minimum horizontal force required to start the box in motion must be equal to or greater than the maximum static friction force calculated in the previous step. Conclude that the monkey must apply a horizontal force equal to the maximum static friction force to overcome it and start the box moving.

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 15th Edition

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

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Young & Freedman Calc 15th Edition

Ch 05: Applying Newton's Laws

Problem 26c

Chapter 5, Problem 26c

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?

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Determine the maximum static friction force using the formula:

f_{s} = μ_{s} N_{}

, where

μ_{s}

is the coefficient of static friction and

N_{}

is the normal force.

Since the box is on a horizontal surface and there is no vertical motion, the normal force

N_{}

is equal to the weight of the box, which is 40.0 N.

Substitute the values into the static friction formula:

f_{s} = 0.40 \times 40.0

. This gives the maximum static friction force.

The minimum horizontal force required to start the box in motion must be equal to or greater than the maximum static friction force calculated in the previous step.

Conclude that the monkey must apply a horizontal force equal to the maximum static friction force to overcome it and start the box moving.

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Key Concepts

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

Weight and Normal Force

The weight of an object is the force due to gravity acting on it, measured in newtons (N). For an object resting on a horizontal surface, the normal force is equal in magnitude and opposite in direction to the weight, providing the support necessary to prevent the object from accelerating downward.

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It is characterized by a coefficient of static friction, which, when multiplied by the normal force, gives the maximum static frictional force that must be overcome to start moving the object.

Kinetic Friction

Kinetic friction occurs when two surfaces slide against each other. It is generally less than static friction and is characterized by a coefficient of kinetic friction. This force acts to oppose the motion of the object once it has started moving, and it is calculated using the normal force and the coefficient of kinetic friction.

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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?

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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 the monkey applies a horizontal force of $18.0$ N, what is the magnitude of the friction force and what is the box's acceleration?

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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 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?

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Textbook Question

A $45.0$ -kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. What are the coefficients of static and kinetic friction between the crate and the floor?

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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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