Question

You drop a rock from a cliff. If air resistance is neglected, which of the following statements is (are) true? 1\. The speed of the rock will increase. 2\. The speed of the rock will decrease. 3\. The acceleration of the rock will increase. 4\. The acceleration of the rock will decrease. a) 1 b) 1 and 4 c) 2 d) 2 and 3

Short answer

Question: A rock is dropped from a cliff without air resistance. Analyze the following statements and determine which one is true: 1) The speed of the rock will increase. 2) The speed of the rock will decrease. 3) The acceleration of the rock will increase. 4) The acceleration of the rock will decrease. Answer: a) 1

Step-by-step solution

Analyze the statements and identify gravity's effect

When a rock is dropped from a cliff, gravity acts on the rock, pulling it downward. Since there is no air resistance, gravity is the only force acting on the rock. So, we need to analyze the statements one by one in relation to gravity and the rock's motion.

Analyze statement 1

The first statement is: "The speed of the rock will increase." As gravity acts on the rock, it will cause the rock to accelerate towards the ground. This means that the speed of the rock will indeed increase with time. So, statement 1 is true.

Analyze statement 2

The second statement is: "The speed of the rock will decrease." This statement is contradictory to the first statement. Since we have concluded that the speed of the rock will increase due to gravity, this statement is false.

Analyze statement 3

The third statement is: "The acceleration of the rock will increase." The acceleration of the rock is due to gravity, which is a constant value (approximately 9.81 m/s^2 on Earth). Since this value does not change, the acceleration of the rock will not increase. Therefore, statement 3 is false.

Analyze statement 4

The fourth statement is: "The acceleration of the rock will decrease." As discussed earlier, the acceleration of the rock is due to gravity, which remains constant. Therefore, the acceleration of the rock will not decrease either. So, statement 4 is false as well.

Determine the correct answer

Based on our analysis, only statement 1 is true. Thus, the correct answer is a) 1.

Key concepts

Gravity

Gravity is the force of attraction between two bodies due to their masses. It's what keeps us anchored to the Earth and dictates the trajectory of celestial bodies in space. In the context of the exercise, gravity is the sole force acting on the rock as it falls from the cliff. Since Earth's gravity is a constant force, it pulls objects towards the center of the Earth at a consistent rate, known as the acceleration due to gravity, often represented as \( g \).

This constant acceleration is approximately \( 9.81 \, \text{m/s}^2 \) on Earth's surface and remains the same regardless of the object's mass. This is why different objects, irrespective of their weight, fall at the same rate in a vacuum where there is no air resistance to alter their motion. In simple terms, gravity is like an invisible hand that steadily pushes objects downward when they are in free fall.

Constant Acceleration

Constant acceleration refers to a steady change in velocity over time. In the case of our free-falling rock from the cliff, the constant acceleration due to gravity causes the rock's speed to increase by the same amount every second. Mathematically, acceleration \( a \) is defined as the rate of change of velocity \( v \) over time \( t \), or \( a = \frac{\Delta v}{\Delta t} \).

For our rock, the acceleration due to gravity (\( g \) or \( 9.81 \, \text{m/s}^2 \) on Earth) remains constant throughout the rock's descent, meaning the increase in the rock's speed is uniform each second. This is a fundamental principle of motion that applies universally to any object in free fall near the Earth's surface, where air resistance can be ignored.

Motion Without Air Resistance

The concept of motion without air resistance, also known as free fall, is an idealized condition where the only force acting on an object is gravity. In reality, when things fall through the air, they experience a frictional force that opposes their motion, known as air resistance. However, in our exercise, we neglect air resistance to simplify the situation and focus on the effect of gravity alone.

When air resistance is absent, all objects, regardless of their size, shape, or weight, fall at the same acceleration due to gravity. This is beautifully demonstrated in vacuum conditions, such as those experienced on the Moon or in physics experiments that remove air to approximate a vacuum. Without the complexity of air resistance, motion becomes predictable and follows the laws of classical mechanics, making it much easier to analyze and understand.