Let's analyze the given scenario:
A rock is suspended from a string and moves downward at a constant speed, with air resistance being ignored. We'll consider the forces acting on the rock and determine the correct statement concerning the tension in the string.
### Step-by-Step Analysis:
1. Forces Acting on the Rock:
- Weight (W): The gravitational force acting downward on the rock. This can be calculated as [tex]\( W = mg \)[/tex], where [tex]\( m \)[/tex] is the mass of the rock and [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]).
- Tension (T): The force exerted by the string on the rock, pulling it upward.
2. Constant Speed:
- The rock is moving downward at a constant speed, implying there is no acceleration. According to Newton's First Law, if an object is moving with a constant speed, the net force acting on the object is zero.
3. Net Force:
- Since the net force is zero, the forces acting on the rock must be balanced. Hence, the upward force (tension) must exactly counteract the downward force (weight).
### Equilibrium Condition:
- [tex]\(\text{Upward force (Tension)} = \text{Downward force (Weight)}\)[/tex]
- Mathematically, [tex]\( T = W \)[/tex]
### Conclusion:
1. The tension is equal to the weight of the rock.
This is because for the rock to move downward at a constant speed (implying zero net acceleration), the tension in the string must balance the gravitational force pulling the rock downward.
### Verifying the Given Statements:
- The tension is less than the weight of the rock: This would result in a net downward force causing acceleration, which contradicts the constant speed condition.
- The tension points downward: Tension is a force that acts along the string and points away from the object; thus, it must point upward to counteract the weight.
- The tension is equal to the weight of the rock: This is the correct statement, as the forces must balance to maintain constant speed.
- The tension is zero newtons: If the tension were zero, the only force acting on the rock would be its weight, causing it to accelerate downward, which contradicts the constant speed condition.
Therefore, the correct statement is:
- The tension is equal to the weight of the rock.
