Energy and Friction and Forces

[omgitsmonica]

Homework Statement

A stack of books rests on a level frictionless surface. A force F acts on the stack, and it accelerates at 4 m/s2. A 9 kg book is then added to the stack. The same force is applied, and now the stack accelerates at 2.5 m/s2. What was the mass in kg of the original stack?

Homework Equations

KE = 1/2mv^2
W = FD

The Attempt at a Solution

I don't even know where to begin with this problem. Neither of the two equations is doable because I'm lacking necessary information, and that's all that's in the textbook except for Hooke's Law.

 

[CompuChip]

Try one of Newton's laws...

 

[baba89]

I would approach this problem by first identifying the known information and the unknown quantity. In this case, the known information is the acceleration of the stack (4 m/s2 and 2.5 m/s2), the mass of the added book (9 kg), and the force applied. The unknown quantity is the mass of the original stack.

Next, I would use the equation F=ma to solve for the force applied to the original stack before the book was added. Since the force applied is the same in both cases, we can set the two equations equal to each other and solve for the original mass:

ma = ma + 9(2.5)
4m = (m+9)(2.5)
4m = 2.5m + 22.5
1.5m = 22.5
m = 15 kg

Therefore, the mass of the original stack was 15 kg. This approach utilizes the concept of Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass. By setting up and solving the equations, we can determine the mass of the original stack without needing to use the equations for kinetic energy or work.