Question
The exact value of the acceleration due to gravity (g) varies with altitude and the makeup of the ground.
Suppose a spring scale is stretched 18 cm by a 100-gram mass at sea level. The acceleration due to gravity atop Mount Everest is 0.3% smaller than at sea level. How will this affect the displacement measured by the spring scale?
(1 point)
Responses
The displacement will decrease by the square of 0.3, or 0.09%.
The displacement will decrease by the square of 0.3, or 0.09%.
Because the value of g decreased, the displacement increased by the same amount, 0.3%.
Because the value of g decreased, the displacement increased by the same amount, 0.3%.
The displacement will also be 0.3% smaller.
The displacement will also be 0.3% smaller.
Because the mass is constant at 100 grams, the displacement will not change.
Suppose a spring scale is stretched 18 cm by a 100-gram mass at sea level. The acceleration due to gravity atop Mount Everest is 0.3% smaller than at sea level. How will this affect the displacement measured by the spring scale?
(1 point)
Responses
The displacement will decrease by the square of 0.3, or 0.09%.
The displacement will decrease by the square of 0.3, or 0.09%.
Because the value of g decreased, the displacement increased by the same amount, 0.3%.
Because the value of g decreased, the displacement increased by the same amount, 0.3%.
The displacement will also be 0.3% smaller.
The displacement will also be 0.3% smaller.
Because the mass is constant at 100 grams, the displacement will not change.
Answers
GPT-4o mini
To determine how the displacement measured by the spring scale will be affected by the change in the acceleration due to gravity (g) on top of Mount Everest, let's analyze the situation.
The force exerted by an object due to gravity is given by the formula:
\[ F = m \cdot g \]
where:
- \( F \) is the force (weight) in newtons,
- \( m \) is the mass in kilograms, and
- \( g \) is the acceleration due to gravity in m/s².
At sea level, with a mass of 100 grams (0.1 kg), the force is:
\[ F_{\text{sea level}} = 0.1 \, \text{kg} \cdot g_{\text{sea level}} \]
On top of Mount Everest, the acceleration due to gravity \( g \) is 0.3% smaller. This means:
\[ g_{\text{Mount Everest}} = g_{\text{sea level}} \cdot (1 - 0.003) \]
This decrease in g means that the force on the same mass will also decrease because the mass remains constant (100 grams). As a result, the displacement measured by the spring scale (which is essentially a measure of the force applied to it) will also decrease.
To quantify:
1. If \( g \) decreases by 0.3%, the new force on the mass will be:
\[ F_{\text{Mount Everest}} = 0.1 \, \text{kg} \cdot g_{\text{sea level}} \cdot (1 - 0.003) = F_{\text{sea level}} \cdot (1 - 0.003) \]
2. The spring scale measures force, thus the scale reading (and hence the displacement) will also decrease by approximately 0.3%.
Therefore, the correct response is:
- The displacement will also be 0.3% smaller.
The force exerted by an object due to gravity is given by the formula:
\[ F = m \cdot g \]
where:
- \( F \) is the force (weight) in newtons,
- \( m \) is the mass in kilograms, and
- \( g \) is the acceleration due to gravity in m/s².
At sea level, with a mass of 100 grams (0.1 kg), the force is:
\[ F_{\text{sea level}} = 0.1 \, \text{kg} \cdot g_{\text{sea level}} \]
On top of Mount Everest, the acceleration due to gravity \( g \) is 0.3% smaller. This means:
\[ g_{\text{Mount Everest}} = g_{\text{sea level}} \cdot (1 - 0.003) \]
This decrease in g means that the force on the same mass will also decrease because the mass remains constant (100 grams). As a result, the displacement measured by the spring scale (which is essentially a measure of the force applied to it) will also decrease.
To quantify:
1. If \( g \) decreases by 0.3%, the new force on the mass will be:
\[ F_{\text{Mount Everest}} = 0.1 \, \text{kg} \cdot g_{\text{sea level}} \cdot (1 - 0.003) = F_{\text{sea level}} \cdot (1 - 0.003) \]
2. The spring scale measures force, thus the scale reading (and hence the displacement) will also decrease by approximately 0.3%.
Therefore, the correct response is:
- The displacement will also be 0.3% smaller.