A stack of books rests on a level perfectly smooth surface. A force F acts on the stack and it acclerated at 3m/s^2. A 1kg book is added to the stack. The same force is applied and now the stack accelerates at 2m/s^2. What was the mass of the original stack?
I think i would use F=ma and F=m_total*a
I chose 5N to be the applied force. so F=ma
5=m(3)
m=1.66
then F=m_total*a
5=(1.66+1)(2)
5=5.32
But this isn't valid. What am I doing wrong?
To solve this problem, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a).
Let's define a few variables:
F1 = force applied before the 1kg book was added
a1 = acceleration before the 1kg book was added
m_stack = mass of the original stack
m_book = mass of the 1kg book
Now, we can set up two equations based on the given information:
Equation 1: F1 = (m_stack * a1)
Equation 2: F1 = ((m_stack + m_book) * a2)
Substituting the given values into these equations, we have:
Equation 1: F1 = (m_stack * 3)
Equation 2: F1 = ((m_stack + 1) * 2)
Since both equations equal F1, we can set them equal to each other:
(m_stack * 3) = ((m_stack + 1) * 2)
Now, let's solve this equation step by step:
Expanding the equation:
3m_stack = 2(m_stack + 1)
Simplifying:
3m_stack = 2m_stack + 2
Bringing the like terms together:
3m_stack - 2m_stack = 2
Simplifying further:
m_stack = 2
Therefore, the mass of the original stack is 2 kg.