A monkey is sitting on a tree limb. The limb exerts a normal force of 48 N and a frictional force of 20 N. Find the magnitude of the total force exerted by the limb on the monkey.

Explanation

To find the magnitude of the total force exerted by the limb on the monkey, we can follow these steps:

### Step 1: Identify the Forces
The limb exerts two forces on the monkey:
- Normal force (N) = 48 N (acting perpendicular to the limb)
- Frictional force (F) = 20 N (acting parallel to the limb)

### Step 2: Understand the Geometry
The normal force and the frictional force are perpendicular to each other. This means we can represent them as two sides of a right triangle where:
- One side is the normal force (N)
- The other side is the frictional force (F)

### Step 3: Apply the Pythagorean Theorem
To find the total force (R) exerted by the limb on the monkey, we can use the Pythagorean theorem:
\[ R = \sqrt{N^2 + F^2} \]

### Step 4: Substitute the Values
Substituting the values of the forces into the equation:
\[ R = \sqrt{(48 \, \text{N})^2 + (20 \, \text{N})^2} \]

### Step 5: Calculate the Squares
Calculate the squares of the forces:
- \( (48 \, \text{N})^2 = 2304 \, \text{N}^2 \)
- \( (20 \, \text{N})^2 = 400 \, \text{N}^2 \)

### Step 6: Add the Squares
Now add the squares:
\[ R^2 = 2304 \, \text{N}^2 + 400 \, \text{N}^2 = 2704 \, \text{N}^2 \]

### Step 7: Take the Square Root
Now take the square root to find R:
\[ R = \sqrt{2704 \, \text{N}^2} = 52 \, \text{N} \]

### Final Answer
The magnitude of the total force exerted by the limb on the monkey is **52 N**.

---