Two forces of mangitude `F_(1)` and `F_(2)` are acting on an object.The magnitude of the net force `F_(n e t )` on the object will be in the range.

Options

A. `F_(1) le F_("net") le F_(2)`
B. `|F_(1) - F_(2)| //2le F_("net") le (F_(1) + F_(2) ) //2`
C. `|F_(1) -F_(2) | le F_("net") le F_(1) + F_(2)`
D. `|F_(1) - F_(2) |ge F_("net") | F_(1) + F_(2) |`

Answer

To determine the range of the net force \( F_{\text{net}} \) acting on an object due to two forces \( F_1 \) and \( F_2 \), we can use the principles of vector addition. Here’s the step-by-step solution:

### Step 1: Understand Vector Addition
When two forces are acting on an object, the resultant or net force can be calculated using vector addition. The formula for the magnitude of the resultant force \( F_{\text{net}} \) when two forces are acting at an angle \( \theta \) to each other is given by:
\[ F_{\text{net}} = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta} \]

### Step 2: Determine Maximum Value
The maximum value of \( F_{\text{net}} \) occurs when the two forces are in the same direction, which means \( \cos \theta = 1 \). Therefore, the maximum net force can be calculated as:
\[ F_{\text{max}} = F_1 + F_2 \]

### Step 3: Determine Minimum Value
The minimum value of \( F_{\text{net}} \) occurs when the two forces are in opposite directions, which means \( \cos \theta = -1 \). Thus, the minimum net force can be calculated as:
\[ F_{\text{min}} = |F_1 - F_2| \]

### Step 4: Establish the Range
From the above calculations, we can establish that the magnitude of the net force \( F_{\text{net}} \) will lie within the range:
\[ |F_1 - F_2| \leq F_{\text{net}} \leq F_1 + F_2 \]

### Conclusion
Thus, the magnitude of the net force \( F_{\text{net}} \) on the object will be in the range:
\[ F_{\text{min}} \leq F_{\text{net}} \leq F_{\text{max}} \quad \text{or} \quad |F_1 - F_2| \leq F_{\text{net}} \leq F_1 + F_2 \]