To solve the problem, we will use the following relevant equations and concepts:
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The force of gravity (weight) can be calculated using the formula: \[ F_{\text{gravity}} = m \cdot g \] where \( m \) is the mass and \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) on the surface of the Earth).
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The net force can be determined by using the equation: \[ F_{\text{net}} = F_{\text{gravity}} - F_{\text{air resistance}} \] Here we consider the upward air resistance opposing the downward force of gravity.
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The acceleration can be calculated using Newton’s second law: \[ F_{\text{net}} = m \cdot a \] Rearranging this gives: \[ a = \frac{F_{\text{net}}}{m} \]
Let's go through each part step by step.
(a) What is the force of gravity on Ancilla?
Given:
- Mass (\( m \)) = 57 kg
- Acceleration due to gravity (\( g \)) = 9.81 m/s²
Calculating the force of gravity: \[ F_{\text{gravity}} = m \cdot g = 57 , \text{kg} \cdot 9.81 , \text{m/s}^2 \approx 559.17 , \text{N} \]
(b) What is the net force on Ancilla?
Given:
- Air resistance (\( F_{\text{air resistance}} \)) = 670 N (upward)
Calculating the net force: \[ F_{\text{net}} = F_{\text{gravity}} - F_{\text{air resistance}} \] Substituting the values: \[ F_{\text{net}} = 559.17 , \text{N} - 670 , \text{N} \approx -110.83 , \text{N} \]
(c) What is Ancilla’s acceleration?
Using the net force calculated: \[ a = \frac{F_{\text{net}}}{m} = \frac{-110.83 , \text{N}}{57 , \text{kg}} \approx -1.94 , \text{m/s}^2 \]
Summary of Results:
(a) The force of gravity on Ancilla is approximately \( 559.17 , \text{N} \) [down].
(b) The net force on Ancilla is approximately \( -110.83 , \text{N} \) [indicating upward direction].
(c) Ancilla’s acceleration is approximately \( -1.94 , \text{m/s}^2 \) [upward].