There are two books on top of one another sitting on a table in an elevator movi
ID: 2096591 • Letter: T
Question
There are two books on top of one another sitting on a table in an elevator moving upwards. The mass of the top book m1 = 9.5 kg and the mass of the bottom book m2 = 2.5 kg. The normal force acting between the table and the bottom book is 70 N. Find the magnitude and the direction of the elevator's acceleration.
I already know the answer from the back of the book, but I always have a little trouble understanding normal force and gravitational force. The answer is -4.0 m/s^2. I really like the steps on how to solve it. I got a close answer, but I know that is not right because I found it in units of mass, not acceleration. Please and thank you.
Explanation / Answer
Here, acceleration is upwards..
forces acting upwards :: normal force between the bottom book and the floor
but the normal force between the books is internal to our reference.
First of all we, need to identify our system and reference.
Here, essentially we are looking at the two books together.
SO, external force to the books are Normal(acting upwards ) & the gravitational force acting downwards. But the two book are moving & accelearating downwards which means normal force (70 N) is smaller than the (m1 + m2)g N
So,70- (m1+m2)g=(m1+m2)a;
solve for a = -4m/s ..
the negative sign comes because, we have taken the upwards direction as positive..