To solve the problem, we need to determine the frictional force exerted by the surface on block Q when a force is applied to block P. Here’s a step-by-step solution:
### Step 1: Identify the given data
- Mass of block P (m₁) = 5 kg
- Mass of block Q (m₂) = 10 kg
- Applied force on block P (F) = 25 N
- Acceleration due to gravity (g) = 10 m/s²
### Step 2: Calculate the normal forces acting on both blocks
The normal force (N) acting on each block can be calculated using the formula:
\[ N = m \cdot g \]
For block P:
\[ N_P = m_1 \cdot g = 5 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 50 \, \text{N} \]
For block Q:
\[ N_Q = m_2 \cdot g = 10 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 100 \, \text{N} \]
### Step 3: Determine the maximum static friction for both blocks
Assuming the coefficients of static friction (μ_s) are given as follows:
- For block P, μ_s = 0.4
- For block Q, μ_s = 0.5
The maximum static friction force (F_s) can be calculated using:
\[ F_s = \mu_s \cdot N \]
For block P:
\[ F_{sP} = \mu_{sP} \cdot N_P = 0.4 \cdot 50 \, \text{N} = 20 \, \text{N} \]
For block Q:
\[ F_{sQ} = \mu_{sQ} \cdot N_Q = 0.5 \cdot 100 \, \text{N} = 50 \, \text{N} \]
### Step 4: Analyze the forces acting on block P
The net force acting on block P is the applied force minus the friction force acting on it. The friction force on block P will be equal to the friction force on block Q since they are in contact and block Q will resist the motion of block P.
Let \( F_{friction} \) be the friction force exerted by block Q on block P. According to Newton's third law:
\[ F_{friction} = F_{sQ} \]
### Step 5: Calculate the frictional force on block Q
Since the applied force on block P is 25 N and the maximum static friction on block P is 20 N, the friction force on block Q will be equal to the net force acting on block P.
The net force acting on block P can be calculated as:
\[ F_{net} = F - F_{sP} = 25 \, \text{N} - 20 \, \text{N} = 5 \, \text{N} \]
Thus, the frictional force exerted by the surface on block Q is:
\[ F_{friction} = 5 \, \text{N} \]
### Final Answer
The frictional force exerted by the surface on block Q is **5 N**.
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