A child weighing 25 kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is 2 N , what is the acceleration of the child

Options

A. `22.5m//s^(2)`
B. `8m//s^(2)`
C. `5m//s^(2)`
D. `9.72m//s^(2)`

Answer

To solve the problem of a child weighing 25 kg sliding down a rope with a friction force of 2 N acting against him, we can follow these steps:

### Step 1: Identify the forces acting on the child
The forces acting on the child are:
- The gravitational force (weight) acting downward, which can be calculated using the formula:
\[ F_g = m \cdot g \]
where \( m = 25 \, \text{kg} \) (mass of the child) and \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

### Step 2: Calculate the gravitational force
Substituting the values into the formula:
\[ F_g = 25 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 245 \, \text{N} \]

### Step 3: Determine the net force acting on the child
The net force (\( F_{net} \)) acting on the child is the difference between the gravitational force and the friction force:
\[ F_{net} = F_g - F_r \]
where \( F_r = 2 \, \text{N} \) (friction force).

### Step 4: Substitute the values to find the net force
\[ F_{net} = 245 \, \text{N} - 2 \, \text{N} = 243 \, \text{N} \]

### Step 5: Apply Newton's second law to find the acceleration
According to Newton's second law, the acceleration (\( a \)) can be calculated using the formula:
\[ a = \frac{F_{net}}{m} \]

### Step 6: Substitute the values to find the acceleration
\[ a = \frac{243 \, \text{N}}{25 \, \text{kg}} = 9.72 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the child sliding down the rope is \( 9.72 \, \text{m/s}^2 \).

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