To find the friction force acting on the block, we will follow these steps:
### Step 1: Identify the forces acting on the block
The block has the following forces acting on it:
- Weight (W) acting downward: \( W = mg \)
- Applied force (F) of 30 N at an angle of 53° downward from the horizontal.
- Normal force (N) acting upward from the surface.
- Frictional force (f) acting opposite to the direction of motion.
### Step 2: Calculate the weight of the block
Given:
- Mass of the block, \( m = 20 \, \text{kg} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)
The weight of the block is calculated as:
\[
W = mg = 20 \, \text{kg} \times 10 \, \text{m/s}^2 = 200 \, \text{N}
\]
### Step 3: Resolve the applied force into its components
The applied force \( F = 30 \, \text{N} \) has two components:
- Horizontal component: \( F_x = F \cos(53^\circ) \)
- Vertical component: \( F_y = F \sin(53^\circ) \)
Calculating these components:
\[
F_x = 30 \cos(53^\circ) = 30 \times \frac{3}{5} = 18 \, \text{N}
\]
\[
F_y = 30 \sin(53^\circ) = 30 \times \frac{4}{5} = 24 \, \text{N}
\]
### Step 4: Calculate the normal force
The normal force \( N \) is affected by both the weight of the block and the vertical component of the applied force. The equation for the normal force is:
\[
N = W + F_y = 200 \, \text{N} + 24 \, \text{N} = 224 \, \text{N}
\]
### Step 5: Calculate the maximum frictional force
The maximum frictional force \( f_{\text{max}} \) can be calculated using the coefficient of friction \( \mu \):
\[
f_{\text{max}} = \mu N
\]
Given \( \mu = 0.2 \):
\[
f_{\text{max}} = 0.2 \times 224 \, \text{N} = 44.8 \, \text{N}
\]
### Step 6: Compare the applied horizontal force and maximum frictional force
The applied horizontal force is \( F_x = 18 \, \text{N} \) and the maximum frictional force is \( f_{\text{max}} = 44.8 \, \text{N} \).
Since \( f_{\text{max}} > F_x \), the block will not move. Therefore, the frictional force \( f \) will equal the applied force:
\[
f = F_x = 18 \, \text{N}
\]
### Final Answer
The friction force acting on the block by the ground is \( 18 \, \text{N} \).
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