Stuck on algebra to N2L solution

In summary, the conversation is about someone struggling with an algebra problem in their physics textbook. They are specifically having trouble with the solution to a problem involving Newton's Second Law (N2L) and friction (f). The solution involves simplifying four N2L equations and solving for f. It is suggested to solve two of the equations for a and then plug that into the third equation to solve for f.
  • #1
NamaeKana
16
0
I already understand the problem, but am having trouble with the algebra for textbook Fund of Physics Solutions, Halliday, 8e, Ch6 Prob 34. Copied here

http://i56.tinypic.com/20uwhw4.jpg

I've been staring at this solution to N2L for hours and can't figure out how to go from the top 4 N2L equations to the bottom equation for f (friction). I tried making both 'as' and 'ab' as 'a' but keep geting back to the orig equation.

Just give me a hint, please...
 
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  • #2
o.k., i typed it here, but it's cryptic with (subscripts)

these four N2L equations:

-f = m(s) a(s)
F(ns) -F(Nb) -m(s)g = 0
f - F = m(b) a(b)
F(Nb) - m(b) g

are shown in the soln to resolve to

f = ( m(s) F ) / ( (m(s) + m(b) )

where do i begin ?
 
  • #3
How are the slab and block related?
 
  • #4
oh ! now i see. it's checking if the block on top is sliding on the slab. not deriving it.
 
  • #6
NamaeKana said:
o.k., i typed it here, but it's cryptic with (subscripts)

these four N2L equations:

-f = m(s) a(s)
F(ns) -F(Nb) -m(s)g = 0
f - F = m(b) a(b)
F(Nb) - m(b) g

are shown in the sol'n to resolve to

f = ( m(s) F ) / ( (m(s) + m(b) )

where do i begin ?

What have you tried?

The solution says that as = ab, they drop the subscripts & simply call them both "a".

Solve the 1st equation for a: [tex]a=\frac{-f}{m_s}\ .[/tex]

Solve the 3rd equation for a: [tex]a=\frac{f-F}{m_b}\ .[/tex]

Set the right hand sides equal to each other & solve for f .

Added in Edit:

It's probably easier Algebra-wise to do the following.

Solve the 1st equation for f:  f = -ms·a

Plug this into the 3rd equation:  -ms·a -F = mb·a

Solve for a, then plug that back into the equation: f = -ms·a
 
Last edited:
  • #7
thanks. i wouldn't have figured that out by myself in a millions years ;-). i get the logic, solve 1 & 3 for a, then take a and plug back into 1.
 

1. What is the N2L solution in algebra?

The N2L (Newton's Second Law) solution in algebra is a mathematical equation used to calculate the net force acting on an object. It is derived from Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. The N2L solution is commonly used in physics and engineering to solve problems involving forces and motion.

2. How do I use the N2L solution in algebra?

To use the N2L solution in algebra, you first need to identify the mass and acceleration of the object in question. Then, you can plug these values into the equation F = ma (where F is net force, m is mass, and a is acceleration) to calculate the net force acting on the object. Make sure to use consistent units for mass (usually in kilograms) and acceleration (usually in meters per second squared) to get an accurate result.

3. Can the N2L solution be used for any type of force?

No, the N2L solution is specifically used for calculating the net force acting on an object. It cannot be used for other types of forces, such as tension or friction. However, if these forces are known, they can be included in the equation to find the net force.

4. What are the limitations of the N2L solution in algebra?

The N2L solution is based on ideal conditions and does not take into account real-world factors such as air resistance and friction. It also assumes that the mass of the object remains constant. Additionally, the N2L solution is only applicable to situations where the net force is constant and in a straight line.

5. How is the N2L solution related to other equations in physics?

The N2L solution is related to other equations in physics, including Newton's First and Third Laws of Motion and the Law of Universal Gravitation. These laws and equations all work together to describe the behavior of objects in motion and the forces acting on them. The N2L solution is also closely related to the concept of inertia, which is the tendency of an object to resist changes in its motion.

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