Question

question 15 (1 point)
a stack of books rests on a level frictionless surface. a force f acts on the stack, and it accelerates at 3.0 m/s2. a 1.0 kg book is then added to the stack. the same force is applied, and now the stack accelerates at 2.0 m/s2. what was the mass of the original stack?
1.0 kg
2.0 kg
3.0 kg
none of the above

Explanation:

Step1: Define variables and apply Newton's second law

Let the mass of the original stack be \( m \) (in kg). According to Newton's second law \( F = ma \), initially, the force \( F \) acting on the stack with mass \( m \) and acceleration \( a_1 = 3.0\ m/s^2 \) gives \( F = m\times3.0 \).

After adding a \( 1.0\ kg \) book, the new mass is \( m + 1.0 \) kg, and the acceleration is \( a_2 = 2.0\ m/s^2 \). So, \( F=(m + 1.0)\times2.0 \).

Step2: Set the two expressions for F equal

Since the force \( F \) is the same in both cases, we can set the two equations equal:
\( 3.0m=2.0(m + 1.0) \)

Step3: Solve for m

Expand the right - hand side: \( 3.0m = 2.0m+2.0 \)
Subtract \( 2.0m \) from both sides: \( 3.0m-2.0m=2.0m + 2.0-2.0m \)
Which simplifies to \( m = 2.0\ kg \)

Answer:

2.0 kg (corresponding to the option "2.0 kg")