Question 371 of 949
A 10 kg box is resting on a flat surface. If the only forces acting on the box are its weight and the normal force from the surface, what can be said about the equilibrium of forces acting on the box?
- The box is accelerating downward.
- The net force acting on the box is zero.
- The normal force is greater than the weight of the box.
- The box is in motion.
Correct Answer:
B
Explanation
### Correct Option: B. The net force acting on the box is zero.
#### Detailed Explanation:
To understand why option B is correct, we need to analyze the situation of the box resting on a flat surface.
1. **Understanding Forces**:
- The box has a weight, which is the force due to gravity acting on it. The weight (W) can be calculated using the formula:
\[
W = m \cdot g
\]
where \( m \) is the mass of the box (10 kg) and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). Thus, the weight of the box is:
\[
W = 10 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 98.1 \, \text{N}
\]
2. **Normal Force**:
- The normal force (N) is the force exerted by the surface that supports the weight of the box. When the box is at rest on a flat surface, the normal force acts vertically upward, opposing the weight of the box.
3. **Equilibrium Condition**:
- For an object to be in equilibrium, the net force acting on it must be zero. This means that all the forces acting on the object must balance each other out. In this case, we have:
- Weight acting downward: \( W = 98.1 \, \text{N} \)
- Normal force acting upward: \( N \)
Since the box is at rest, we can conclude that:
\[
N = W
\]
Therefore, the normal force is also \( 98.1 \, \text{N} \).
4. **Net Force Calculation**:
- The net force (F_net) acting on the box can be calculated as:
\[
F_{\text{net}} = N - W
\]
Substituting the values:
\[
F_{\text{net}} = 98.1 \, \text{N} - 98.1 \, \text{N} = 0 \, \text{N}
\]
Since the net force is zero, the box is in a state of equilibrium.
#### Why Other Options Are Incorrect:
- **Option A: The box is accelerating downward.**
- This option is incorrect because if the box were accelerating downward, it would mean that the net force acting on it is not zero. In our case, since the forces are balanced (normal force equals weight), there is no acceleration.
- **Option C: The normal force is greater than the weight of the box.**
- This option is also incorrect. For the box to be at rest on a flat surface, the normal force must equal the weight of the box. If the normal force were greater than the weight, the box would not be in equilibrium and would accelerate upward, which is not the case here.
- **Option D: The box is in motion.**
- This option is incorrect because the problem states that the box is resting on the surface. If it were in motion, it would not be at rest, contradicting the given information.
### Revision Summary:
- The box is in equilibrium because the net force acting on it is zero.
- The weight of the box (98.1 N) is balanced by the normal force (also 98.1 N).
- An object at rest on a flat surface experiences equal and opposite forces, leading to no acceleration.
- Understanding the balance of forces is crucial for analyzing static equilibrium situations.