If a body is moving with constant velocity, then what is the force applied F on the body of mass M?

Options

A. `F=ma`
B. `F=f_k`
C. `F=0`
D. None of these

Answer

To solve the problem, we need to analyze the situation where a body of mass \( M \) is moving with a constant velocity. The key points to consider are:

1. **Understanding Constant Velocity**: When a body is moving with constant velocity, it means that its acceleration is zero. According to Newton's first law of motion, if the net force acting on an object is zero, the object will continue to move at a constant velocity.

2. **Identifying Forces**: In this scenario, the body experiences two main forces:
- An applied force \( F \) in the direction of motion.
- A frictional force \( F_k \) acting in the opposite direction (backward).

3. **Applying Newton's Second Law**: According to Newton's second law, the net force \( F_{net} \) acting on the body can be expressed as:
\[ F_{net} = F - F_k \]
Since the body is moving with constant velocity, we know that \( F_{net} = 0 \).

4. **Setting Up the Equation**: Since \( F_{net} = 0 \), we can set up the equation:
\[ F - F_k = 0 \]

5. **Solving for the Applied Force**: Rearranging the equation gives us:
\[ F = F_k \]
This means that the applied force \( F \) must equal the kinetic frictional force \( F_k \) acting on the body.

6. **Conclusion**: Therefore, if a body is moving with constant velocity, the force applied \( F \) on the body of mass \( M \) is equal to the kinetic frictional force \( F_k \).

### Final Answer:
The force applied \( F \) on the body of mass \( M \) is equal to the kinetic frictional force \( F_k \).

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