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Ch 05: Applying Newton's Laws
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 05: Applying Newton's LawsProblema 26a
Capitolo 5, Problema 26a

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?

Guida verificata passo dopo passo
1
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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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.
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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.
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The Normal Force

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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