Respuesta :
Answer:
1) The mass of the student is approximately 73.39 kg
2) The net force on the student is approximately 947.523 N
3) The value the scale will read is approximately 96.59 kg
Explanation:
The given parameters are;
The weight of the student = 720 N
The speed at which the elevator is decreasing = 3.1 m/s²
1) The weight of the student = The mass of the student × The acceleration due to gravity
The acceleration due to gravity is a constant = 9.81 m/s²
Substituting the known values gives;
720 N = The mass of the student × 9.81 m/s²
∴ The mass of the student = 720 N/(9.81 m/s²) ≈ 73.39 kg
2) The forces acting on the student are;
i) The force of gravity which is the weight of the student acting downwards
ii) The inertia force of the slowing elevator acting downwards in the same direction as the weight of the student
The net force, [tex]F_{net}[/tex] = The weight of the student + The inertia force of the slowing elevator
∴ The net force, [tex]F_{net}[/tex] = 720 N + 73.39 kg × 3.1 m/s² ≈ 947.523 N
3) The scale will read the mass of the student as follows;
Mass reading of student on the scale = Force on scale/9.81
∴ Mass reading of student on the scale = 947.523/9.81 ≈ 96.59 kg
The value the scale will read = 96.59 kg.
The mass of student is, 73.46 kg.
The net force acting on the student is 942.72 N.
The reading of the scale is 96.70 kg
Given data:
The weight of student is, W = 720 N.
The magnitude of acceleration is, [tex]a = 3.1 \;\rm m/s^{2}[/tex].
The standard expression for the weight is,
[tex]W =mg[/tex]
Here, g is the gravitational acceleration. And m is the mass of student.
Solving as,
[tex]W =mg\\\\720 = m \times 9.8\\\\m = 73.46 \;\rm kg[/tex]
Thus, the mass of student is, 73.46 kg.
Since, the force of gravity which is the weight of the student acting downwards . The inertia force of the slowing elevator acting downwards in the same direction as the weight of the student. Then the net force is,
[tex]F_{net} = W+(ma)[/tex]
Solving as,
[tex]F_{net} = 720+(73.46 \times 3.1)\\\\F_{net}=947.72 \;\rm N[/tex]
Thus, we can conclude that the net force acting on the student is 942.72 N.
The reading of the scale is given as,
[tex]reading=\dfrac{F_{net}}{g}[/tex]
Solving as,
[tex]reading = \dfrac{947.72}{9.8}\\\\reading=96.70 \;\rm kg[/tex]
Thus, we can conclude the reading of the scale is 96.70 kg.
Learn more about the concept of gravitational acceleration here:
https://brainly.com/question/25316208
