A block of mass 1kg lies on a horizontal surface in a truck. The coefficeint of friction between the block and surface is 0.5. If the acceleration of the truck is `6ms^(-2)` the acceleration of the block relative to ground is

Options

A. `6 m//s^(2)`
B. `1.1 m//s^(2)`
C. `4.9 m//s^(2)`
D. `0 m//s^(2)`

Answer

To solve the problem step by step, we will analyze the forces acting on the block and calculate its acceleration relative to the ground.

### Step 1: Identify the given values
- Mass of the block, \( m = 1 \, \text{kg} \)
- Coefficient of friction, \( \mu = 0.5 \)
- Acceleration of the truck, \( a_{\text{truck}} = 6 \, \text{m/s}^2 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

### Step 2: Calculate the maximum static friction force
The maximum static friction force \( F_f \) can be calculated using the formula:
\[ F_f = \mu \cdot m \cdot g \]
Substituting the known values:
\[ F_f = 0.5 \cdot 1 \cdot 9.8 = 4.9 \, \text{N} \]

### Step 3: Calculate the net force acting on the block
The net force \( F_{\text{net}} \) acting on the block can be calculated using Newton's second law:
\[ F_{\text{net}} = m \cdot a_{\text{truck}} - F_f \]
Substituting the values:
\[ F_{\text{net}} = 1 \cdot 6 - 4.9 = 6 - 4.9 = 1.1 \, \text{N} \]

### Step 4: Calculate the acceleration of the block relative to the truck
Using Newton's second law, the acceleration \( a_{\text{block}} \) of the block relative to the truck can be calculated as:
\[ a_{\text{block}} = \frac{F_{\text{net}}}{m} = \frac{1.1}{1} = 1.1 \, \text{m/s}^2 \]

### Step 5: Calculate the acceleration of the block relative to the ground
The acceleration of the block relative to the ground \( a_{\text{ground}} \) is given by:
\[ a_{\text{ground}} = a_{\text{truck}} - a_{\text{block}} \]
Substituting the values:
\[ a_{\text{ground}} = 6 - 1.1 = 4.9 \, \text{m/s}^2 \]

### Conclusion
The acceleration of the block relative to the ground is \( 4.9 \, \text{m/s}^2 \).

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