When a body moves with some friction on a surface

Options

A. It loses kinetic energy but momentum is constant
B. It loses kinetic energy but gains potential energy
C. Kinetic energy and momentum both decrease
D. Mechanical energy is conserved

Explanation

To solve the question regarding the motion of a body with friction on a surface, we will analyze the effects of friction on kinetic energy, momentum, and mechanical energy step by step.

### Step 1: Understand the Forces Acting on the Body
When a body moves on a surface with friction, the frictional force acts in the opposite direction to the motion of the body. This frictional force is a non-conservative force, which means it does work that depends on the path taken by the body.

**Hint:** Identify the direction of the forces acting on the body and their nature (conservative or non-conservative).

### Step 2: Apply the Work-Energy Theorem
According to the work-energy theorem, the net work done on a body is equal to the change in its kinetic energy. In this case, the only external force doing work is the frictional force.

**Hint:** Recall the work-energy theorem: \( W_{net} = \Delta KE \).

### Step 3: Calculate the Work Done by Friction
The work done by the frictional force is negative because it acts in the opposite direction to the displacement of the body. If the frictional force is \( F \) and the displacement is \( d \), the work done \( W \) can be expressed as:
\[ W = F \cdot d \cdot \cos(180^\circ) = -F \cdot d \]
This negative work indicates that energy is being taken away from the system.

**Hint:** Remember that when the force and displacement are in opposite directions, the work done is negative.

### Step 4: Analyze the Change in Kinetic Energy
Since the work done by friction is negative, the change in kinetic energy will also be negative:
\[ \Delta KE = KE_{final} - KE_{initial} < 0 \]
This implies that the final kinetic energy is less than the initial kinetic energy.

**Hint:** A negative change in kinetic energy means the body is losing kinetic energy.

### Step 5: Consider the Momentum of the Body
Momentum is defined as the product of mass and velocity:
\[ p = m \cdot v \]
Since the frictional force acts as a retarding force, it will cause the velocity of the body to decrease. As a result, the momentum will also decrease.

**Hint:** Remember that momentum depends on velocity; if velocity decreases, momentum decreases.

### Step 6: Evaluate Potential Energy
The potential energy of the body can change depending on its position relative to a reference point (e.g., height). However, if the body is moving horizontally on a flat surface, the potential energy remains constant unless there is a vertical displacement.

**Hint:** Consider the context of potential energy changes based on the motion of the body.

### Step 7: Conclusion
Based on the analysis:
- The body loses kinetic energy due to the work done by friction.
- The momentum of the body decreases because of the retarding force of friction.
- The mechanical energy is not conserved because some kinetic energy is transformed into heat due to friction.

Thus, the correct option is that both kinetic energy and momentum decrease.

**Final Answer:** C) Kinetic energy and momentum both decrease.