To solve the problem, we will apply the concepts of force and weight.
(a) What is the force of gravity on Ancilla?
The force of gravity (weight) acting on Ancilla can be calculated using the formula: \[ F_g = m \cdot g \] where \( m \) is the mass of Ancilla (57 kg) and \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)).
Calculating the force of gravity: \[ F_g = 57 , \text{kg} \cdot 9.81 , \text{m/s}^2 \approx 559.17 , \text{N} \]
Answer to (a): The force of gravity on Ancilla is approximately 559 N [down].
(b) What is the net force on Ancilla?
The net force can be calculated by considering the forces acting on Ancilla. The force of gravity acts downwards and the air resistance acts upwards.
Net force is given by: \[ F_{\text{net}} = F_g - F_{\text{air resistance}} \] Given that the force of air resistance is 670 N [up], we can substitute the values: \[ F_{\text{net}} = 559 , \text{N} - 670 , \text{N} = -111 , \text{N} \]
Answer to (b): The net force on Ancilla is -111 N [down].
(c) What is Ancilla’s acceleration?
To find Ancilla's acceleration, we can use Newton's second law: \[ F_{\text{net}} = m \cdot a \] where \( a \) is the acceleration. We can rearrange this to solve for acceleration: \[ a = \frac{F_{\text{net}}}{m} \] Substituting the values we calculated: \[ a = \frac{-111 , \text{N}}{57 , \text{kg}} \approx -1.95 , \text{m/s}^2 \]
Answer to (c): Ancilla’s acceleration is approximately -1.95 m/s² (the negative sign indicates that the acceleration is downward).
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