What Is the Mass of a Book Accelerating on a Wooden Table?

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Homework Help Overview

The problem involves determining the mass of a book that is accelerating on a wooden table, considering the effects of friction. The scenario includes a frictional force and an applied force, with the book accelerating at a specified rate.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the frictional force and the net force in the context of Newton's second law (F=ma). Questions arise regarding how to correctly account for the directions of the forces involved and how to calculate the net force.

Discussion Status

Participants are actively engaging with the problem, clarifying the concept of net force and its calculation. Some guidance has been provided regarding the need to consider the directions of the forces, and there is an ongoing exploration of how to apply the relevant equations.

Contextual Notes

There is a focus on understanding the net force in relation to the applied and frictional forces, with participants questioning the assumptions about how these forces interact. The discussion reflects a learning process without reaching a definitive conclusion.

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Homework Statement


Because of a frictional force of 2.6N, a force of 2.8N must be applied to a textbook in order to slide it along the surface of a wooden table. The book accelerates at a rate of 0.11 m/s

a) What is the unbalanced force on the book?
b) What is the mass of the book?

Homework Equations



The Attempt at a Solution



The frictional force of 2.6 has anything to do with the equation F=ma to find the mass? If yes, what is the equation?
 
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rfurtado said:

The Attempt at a Solution



The frictional force of 2.6 has anything to do with the equation F=ma to find the mass? If yes, what is the equation?

Yes, it does, because 'F' in that equation refers to the NET force on the body (also referred to as the unbalanced force in your homework problem). To calculate the net force, you must consider the applied force and the frictional force, adding them together (taking into account their directions).
 
Oh ok. So you mean that I need to add (the regular addition or in any other way?) the frictional force which is 2.6 and the force of 2.8, and then finish with the regular equation to find the mass?
 
Last edited:
No, obviously not just regular addition. Like I said before, you have to take into account the directions of the forces! The applied force is trying to move the textbook in one direction, eg. to the right. The frictional force is trying to oppose that motion (it points to the left). The two forces are *opposite*, so one of them partly balances out (ie cancels out) the other. The remaining part (which is the NET force acting on the object) is the only thing that is left to actually move the object. Since you know that the acceleration value given in the problem must be due to this "leftover" force, you can deduce the mass of the object.
 
Now I think I got it =) well, I did the equation and got .2N as the remaining force, then I did the regular equation to find the mass.

m= ? ========> m=f/a ==> m=.2/.11= 1.8 kg
a= .11 m/s
f= .2N
 

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