An object of 5 kg is placed on rough surface whose `mu_k=0.3` and `mu_s=0.4`. What is the minimum force required to start movement in 5 kg?

Options

A. 15N
B. 20N
C. 50N
D. 70N

Answer

To solve the problem of finding the minimum force required to start the movement of a 5 kg object on a rough surface, we will follow these steps:

### Step 1: Identify the given values
- Mass of the object (m) = 5 kg
- Coefficient of static friction (μ_s) = 0.4
- Coefficient of kinetic friction (μ_k) = 0.3

### Step 2: Calculate the weight of the object
The weight (W) of the object can be calculated using the formula:
\[ W = m \cdot g \]
Where \( g \) is the acceleration due to gravity, approximately \( 10 \, \text{m/s}^2 \).

Calculating the weight:
\[ W = 5 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 50 \, \text{N} \]

### Step 3: Calculate the maximum static friction force
The maximum static friction force (F_s) that can act on the object before it starts moving is given by:
\[ F_s = \mu_s \cdot N \]
Where \( N \) is the normal force. On a horizontal surface, the normal force is equal to the weight of the object.

Thus,
\[ F_s = \mu_s \cdot W \]
Substituting the values:
\[ F_s = 0.4 \cdot 50 \, \text{N} = 20 \, \text{N} \]

### Step 4: Determine the minimum force required to start movement
The minimum force (F) required to overcome static friction and start the movement of the object is equal to the maximum static friction force:
\[ F = F_s = 20 \, \text{N} \]

### Conclusion
Therefore, the minimum force required to start the movement of the 5 kg object is **20 N**.

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