A ladder wighing 300 N is placed against a smooth vertical wall having a coefficient of friction between it and the floor of 0.2. What is the maximum force of friction available at the point of contact between the ladder and the floor?

Options

A. 40 N
B. 50 N
C. 60 N
D. 70 N

Explanation

To find the maximum force of friction available at the point of contact between the ladder and the floor, we can follow these steps:

### Step 1: Understand the Problem
We have a ladder weighing 300 N placed against a smooth vertical wall. The coefficient of friction between the ladder and the floor is given as 0.2. We need to determine the maximum force of friction at the point of contact between the ladder and the floor.

### Step 2: Identify the Forces Acting on the Ladder
The forces acting on the ladder are:
- The weight of the ladder (W = 300 N) acting downwards.
- The normal reaction force (R) acting upwards at the point of contact with the floor.
- The frictional force (F_friction) acting horizontally at the base of the ladder, opposing any motion.

### Step 3: Apply the Formula for Maximum Frictional Force
The maximum force of friction (F_friction) can be calculated using the formula:
\[ F_{friction} = \mu \cdot R \]
where:
- \( \mu \) is the coefficient of friction (0.2 in this case).
- \( R \) is the normal reaction force.

### Step 4: Determine the Normal Reaction Force
In this scenario, since the ladder is in equilibrium and there are no vertical movements, the normal reaction force (R) is equal to the weight of the ladder:
\[ R = W = 300 \, N \]

### Step 5: Calculate the Maximum Frictional Force
Now, we can substitute the values into the friction formula:
\[ F_{friction} = \mu \cdot R = 0.2 \cdot 300 \, N \]
\[ F_{friction} = 60 \, N \]

### Conclusion
The maximum force of friction available at the point of contact between the ladder and the floor is **60 N**.

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