To solve the problem step by step, we will analyze the forces acting on the blocks A and B in the elevator.
### Step 1: Understand the forces acting on the blocks
- Block A has a mass of \( m_A = 2 \, \text{kg} \).
- Block B has an unknown mass \( m_B \).
- The elevator is accelerating upwards with an acceleration \( a = 2 \, \text{m/s}^2 \).
- The acceleration due to gravity is \( g = 10 \, \text{m/s}^2 \).
### Step 2: Calculate the gravitational force acting on the blocks
The gravitational force acting on block A is:
\[
F_{gA} = m_A \cdot g = 2 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20 \, \text{N}
\]
The gravitational force acting on block B is:
\[
F_{gB} = m_B \cdot g = m_B \cdot 10 \, \text{m/s}^2
\]
### Step 3: Calculate the total gravitational force on the floor of the elevator
The total gravitational force acting on the floor due to both blocks is:
\[
F_g = F_{gA} + F_{gB} = 20 \, \text{N} + (m_B \cdot 10 \, \text{N})
\]
This simplifies to:
\[
F_g = 20 + 10m_B \, \text{N}
\]
### Step 4: Calculate the force due to the upward acceleration of the elevator
The force due to the upward acceleration of the elevator acting on both blocks is:
\[
F_a = (m_A + m_B) \cdot a = (2 + m_B) \cdot 2 \, \text{m/s}^2
\]
This expands to:
\[
F_a = 4 + 2m_B \, \text{N}
\]
### Step 5: Calculate the total force exerted on the floor of the elevator
The total force exerted on the floor of the elevator is the sum of the gravitational force and the force due to acceleration:
\[
F_{total} = F_g + F_a = (20 + 10m_B) + (4 + 2m_B)
\]
Combining these gives:
\[
F_{total} = 24 + 12m_B \, \text{N}
\]
### Step 6: Set up the equation using the given force
According to the problem, the total force exerted on the floor is \( F_{total} = 60 \, \text{N} \). Therefore, we can set up the equation:
\[
24 + 12m_B = 60
\]
### Step 7: Solve for \( m_B \)
Now, we solve for \( m_B \):
\[
12m_B = 60 - 24
\]
\[
12m_B = 36
\]
\[
m_B = \frac{36}{12} = 3 \, \text{kg}
\]
### Final Answer
The mass of block B is \( m_B = 3 \, \text{kg} \).
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