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Chapter 4: Problem 103

Felipe is going for a physical before joining the swim team. He is concerned about his weight, so he carries his scale into the elevator to check his weight while heading to the doctor's office on the 21 st floor of the building. If his scale reads \(750 \mathrm{N}\) while the elevator has an upward acceleration of \(2.0 \mathrm{m} / \mathrm{s}^{2},\) what does the nurse measure his weight to be?

Short Answer

Expert verified
Answer: Felipe's actual weight as measured by the nurse on the 21st floor is approximately 623.07 N.

Step by step solution

01

Determine Felipe's mass in the elevator

In order to find Felipe's mass, we can use the following equation: \(m_{elevator} = \frac{W_{elevator}}{g + a}\) where \(m_{elevator}\) is Felipe's mass in the elevator, \(W_{elevator}\) is his weight as observed in the elevator (750 N), \(g\) is acceleration due to gravity (9.81 m/s虏), and \(a\) is the acceleration of the elevator (2.0 m/s虏). Now, we can plug the values into the equation: \(m_{elevator} = \frac{750 \mathrm{N}}{9.81 \mathrm{m/s虏} + 2.0 \mathrm{m/s虏}}\)
02

Calculate Felipe's mass in the elevator

Solve the equation for \(m_{elevator}\): \(m_{elevator} = \frac{750 \mathrm{N}}{11.81 \mathrm{m/s虏}} = 63.5 \mathrm{kg}\)
03

Calculate Felipe's actual weight

Now that we have Felipe's mass, we can find his actual weight by multiplying it by the acceleration due to gravity (\(g\)): \(W_{actual} = m_{elevator} \times g\) \(W_{actual} = 63.5 \mathrm{kg} \times 9.81 \mathrm{m/s虏}\)
04

Calculate Felipe's measured weight by the nurse

Solve the equation for \(W_{actual}\): \(W_{actual} = 63.5 \mathrm{kg} \times 9.81 \mathrm{m/s虏} = 623.07 \mathrm{N}\) So, the nurse measures Felipe's weight to be approximately 623.07 N.

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