To solve the problems, we'll use the following formulas:
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The force of gravity (weight) acting on an object 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 \( 9.81 , \text{m/s}^2 \)).
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The net force acting on an object can be calculated using Newton's second law: \[ F_{\text{net}} = F_{\text{gravity}} - F_{\text{air resistance}} \] (Here, air resistance acts in the opposite direction of gravity.)
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Finally, the acceleration can be calculated using: \[ a = \frac{F_{\text{net}}}{m} \]
Now, let's calculate each part:
(a) What is the force of gravity on Ancilla?
Using the mass of Ancilla \( m = 57 , \text{kg} \): \[ F_{\text{gravity}} = m \cdot g = 57 , \text{kg} \cdot 9.81 , \text{m/s}^2 \approx 559.17 , \text{N} \] So, the force of gravity on Ancilla is approximately 559 N [down].
(b) What is the net force on Ancilla?
The force of air resistance \( F_{\text{air resistance}} \) is given as \( 670 , \text{N} \) [up]. Now calculate the net force: \[ F_{\text{net}} = F_{\text{gravity}} - F_{\text{air resistance}} = 559 , \text{N} - 670 , \text{N} = -111 , \text{N} \] The negative sign indicates that the net force is directed upward. So, the net force on Ancilla is 111 N [up].
(c) What is Ancilla’s acceleration?
Now using the net force to find the acceleration: \[ a = \frac{F_{\text{net}}}{m} = \frac{-111 , \text{N}}{57 , \text{kg}} \approx -1.95 , \text{m/s}^2 \] The negative acceleration indicates that Ancilla is decelerating (moving upward), so her acceleration is approximately 1.95 m/s² [up].
Summary:
(a) Force of gravity on Ancilla: 559 N [down]
(b) Net force on Ancilla: 111 N [up]
(c) Ancilla’s acceleration: 1.95 m/s² [up]
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